I will fuck your faces you fucktards
The most important tip of all: BE AGGRESSIVE. People in Renegade are very protective of their investments and will oftentimes run away at the first sign of danger to their expensive characters and/or vehicles. If you take advantage of this by chasing them down and killing them, they will be afraid of you and therefore easy to manipulate and slaughter.
To improve the game's internet performance a bit, when you enter a game for the first time, hit the tilde (~) key (it's on the leftmost side under the Escape key) and type C, then hit enter. This turns on Client Physics Optimization, which will improve network performance by only doing background work for people and vehicles that are in your field of vision. Repeating the command turns it off. This tends to improve performance in the field but when in vehicles it will probably make you lag a bit, so you can change it if necessary on the fly.
To show your in-game Frames Per Second (FPS for short), hit the tilde (~) key again and type FPS then hit enter. You'll get a numerical readout of your FPS, your ping (that's a rough measure of your lag, anything above about 200-250 is pretty bad) and your KBPS (the amount of data you're getting from the server each second, on average). This is useful for diagnosing possible problems with your hardware setup or connection.
To improve your aiming with certain characters, sometimes it's better to turn down your Geometry Settings in the Video options to Low. This makes the beam from Mobius/Mendoza and repair guns fire in a straight line instead of a jagged lightning design, which can make it easier to tell if you're actually hitting people and how much you need to lead them by.
If your sound is set up correctly (generally using surround sound is better for this purpose), and it's quiet in the game, you can sometimes hear footsteps from cloaked units. If you hear footsteps and no one is around, it's generally a good idea to investigate.
If you're stuck with a timed C4, either run back to base and buy yourself a vehicle or hop into one of your team's vehicles. If you're in a vehicle when the C4 goes off, you won't take any damage.
Aim for the head. Headshots do 5x damage, so if you can hit 1 out of 5 in the head it's better than 4 out of 5 in the chest. There are, of course, exceptions. If you can kill someone in 2 or 3 body shots, it's not as critical to aim for the head. Headshots are still better in general, though. People who aim for the head will be getting 5x as many kills as everyone else, and that is a group you'd rather be a part of than be against. Many people will accuse you of cheating when they die quickly from headshots. When you figure that most characters with automatic weapons can kill someone in as few as 4 shots to the head, this is understandably a cause of surprise to the average person.
Infantry show up on radar even when they're in a tank when full radar is on. This means that while a stealth tank is invisible on radar, the person inside the tank can still be seen on radar unless they are also a stealth soldier. If you see a fast-moving blip on the radar and no one is in that general direction, pull out your pistol and start firing around because there's a stealth tank somewhere in the vicinity.
If you see the doors to a building open when nobody's around, or if you see a crate/spawn weapon disappear for no reason, start looking around for a SBH.
Remember that on many maps (Canyon, City, Walls in particular, although you can do it on other maps with a little teamwork and ingenuity) people can get on top of the Barracks roof. This makes any mines out in front of the Barracks doors useless; enemies can simply drop down behind them and walk into the building unchallenged. It is generally better to mine the insides of the doors than to mine the outer entrance for this reason.
If you have a vehicle and a vehicle is rushing your base, try to block the enemy vehicle from entering your base. If you can block their vehicle near your base defenses, the obelisk/AGT will kill the vehicle for you, and the enemies that were in it won't have time to get inside a building before the base defenses kill them or you run them over.
Remember that weapons are made for specific purposes. Don't bother trying to kill a flame tank with an auto rifle or a sniper rifle, because you'll just waste all your ammo without making a dent. Likewise, don't use a shotgun or a flamethrower to try to kill someone 50 feet away. Switch to your pistol; it's got better range. If you're curious as to what kinds of weapons are best suited to take out certain types of targets, check the specific character and weapon pages in the Wiki.
Press J to see your team info. This will show you the health of all your buildings as well as what characters/vehicles your teammates have. It will also show their available credits, so you'll know who to invite along on a tank rush.
Press K to see the info for both teams. This gives less detailed information than J, but it will show the health of all of your buildings and all of your enemies' buildings.
Press L to see the server info. This page will show you the server settings (regarding radar type, weapon spawns, etc.) and the name of the current map.
There is a time for team-chat and a time for all-chat. Don't use all-chat to suggest a strategy to the rest of your team.
Never leave your base completely defenseless. An empty base is pathetically easy to nuke/ion, and if the enemy sets one on the pedestal, that's game over on most servers. This is especially critical to remember if you're on GDI, because there may be an SBH just sitting on the pedestal, watching his radar, waiting for you to leave the base.
Use the Radio Commands! Either commit them to memory or make yourself a list on a piece of paper and keep it near the computer when you play. It's a lot quicker use the radio command than it is to type "defend the refinery." Don't spam radio commands, because if you send too many the game won't let you send any messages for a while and people don't listen when you spam commands.
Never let infantry (especially technicians/hotwires) into your base unassailed. If you just assume someone else is going to deal with the problem, you're likely to lose a building very soon. (You may be able to get away with ignoring a rifle soldier or a shotgunner, because they can't do much damage to a building... but then again, you never know who might be carrying a nuke.)
When rushing with an APC, don't kill free characters out in the field (this is the one caveat to letting infantry into your base unmolested). If you kill them, they'll respawn in their base, in prime position to defend against your rush. If you just drive past them, though, they'll do negligible damage to your APC, and they won't be able to get back to base in time to disarm your c4. It is still to your benefit to kill upper-class characters, though, as you will cost them money and gain yourself some points
If you sit still for very long, you'll probably be sniped. Try to keep moving at all times, especially if you yourself are a sniper.
Don't kill empty enemy vehicles in your base unless an enemy is going to take them. Despite the enemy colors on the outside of the tank/APC, your teammates can still get in and drive. Killing an empty enemy APC in your base is just a waste of 500 credits. Also, remember that there is a vehicle limit - only 8 GDI vehicles and 8 Nod vehicles at a time. Also, a GDI medium tank counts towards the 8 GDI vehicles if it's empty, or even if it's been stolen by Nod. This means that sometimes it's a good strategy to stash stolen vehicles in the back of your base instead of using them yourself.
USE TEAMWORK! A coordinated attack is generally much more effective than a solo one. One person can sometimes sneak into a base unnoticed and destroy a building alone, but it's even easier to sneak in when there's a simultaneous tank rush drawing attention away from you. Likewise, coordinated base defenses are MUCH harder to beat than defenders who don't communicate.
When trying to save a building from enemy engineers/hotwires/technicians, it's generally better to repair the building first rather than trying to kill the intruders. Once the building has enough health that it can survive all the remaining c4 on the MCT, then turn your attention to the enemies.
Don't set a beacon unless you can defend it, especially if your team is already winning. The other team gets 300 points for disarming a beacon, so this is an easy way to give away your lead, especially if multiple people on your team are doing it.
When laying a beacon, throw your C4 on top of it. If you can land it perfectly on the beacon, it will make it a lot harder to disarm as the hitbox for the C4 will be in the way of the repair beam. This works best if you've got a Technician or Hotwire and can lay proximity mines on the beacon, but Engineers can do a passable job as well with remotes and a timed C4.
A stealth tank can make a sneaky 1-person APC, especially when the defenses are gone. Bring a nuke for added enjoyment, then park on top of it after you set it. Be sure to exercise your right to run enemies over. This works best if you are also a cloaked soldier so you can still escape if your tank dies, or if you are a technician and can repair your tank and/or mine the nuke to make it harder to disarm.
If you're playing in a smaller game (4v4 or less), it's easy to distract your opponents by making a false EVA warning. This is done by shooting a building you're not going to attack, and then going to work on the one you really want. Most people will see that there is in fact no one at the building that was announced as under attack and go on their merry way, giving you another 15-30 seconds before EVA announces the next building is under attack to do your dirty work.