Lerp is a delay, intentionally added to the game by Valve for smoothing movements of players who use unstable internet connection. Every player is able to set the delay time (100ms or 0.1s by default). Default value is too much exaggerated from what most players need. Actually, it's made for people who use 3G modems for playing multiplayer games.

However, as of 2015, most players have decent PCs with at least 2 cores inside and fast stable connection. Thus, increased lerp value becomes almost useless. The shorter the lerp time is, the more the game state on your screen matches the one on the server. If you have a faster reaction than a 60 year old granny, setting lerp time is what you have to do. Gameplay quality will be greatly increased.

Pros of reducing lerp time:

• Reduced delay between pressing a mouse button and hit registration. (when using accurate weapon)
  
• More realistic Demoman and Soldier projectiles: once a player shoots, the projectile appears right near his gun and flies through the map evenly, instead of spawning in the middle of nowhere and teleporting to your face.
  
• In order to hit a target, you need to aim directly at it, instead of predicting its actions the next split second. Works for both projectiles and bullets.

Cons of reducing lerp time:

• Better server quality is required. In order to provide smooth gameplay, the server must have stable FPS (yes, the server has FPS too) and correct connection settings on its side. Default settings are not considered correct for a good server.
  
• In case of another player having an unstable connection, which is unable to send packets evenly, he will lag on your screen. If you use projectile weapon you will handle it, but in case of really laggy players shooting from accurate weapon will prevent you from killing the target.

You can change your lerp time by using console command cl_interp <time>, where <time> is lerp time in seconds. For example, cl_interp 0.035 (0.035 seconds is 35ms). I advise to try the least value (0) and gradually increase it if you meet any problems. Remember, that TF2 doesn't allow you to change the lerp time midgame: you will have to spectate or disconnect from the server entirely. Also, you will never have real lerp 0 if you set it. Almost all servers force their clients to use at least lerp 15.2ms

Rates is a frequency of data exchange with the server, measured in packets per second. Team Fortress 2 servers (without any special mods) generate game state 66.7 times per second, while clients (game on your PC) are set to 20/s for receiving and 30/s for sending by default. The more often you exchange data, the more the game state on your screen matches the one on the server (logic, ♥♥♥♥♥).

Pros of increasing rates up to 66:

• The movements of other players look smoother.
  
• More accurate hit registration.

There are no disadvantages of increasing rates up to 66, you will meet troubles only if your PC or internet connection can`t handle those settings. For example, if your FPS drops down below 66: obviously, a client is unable to send data more often than it processes frames on your screen. Next, if your connection is too weak you also will experience problems. In the midst of battle the traffic speed can grow up to 50Kb/s (same as 400Kbit/s), if your connection speed is less than this value, there is no point to change default rates. Also, you shouldn`t forget about connection stability: if your ping is jumping from 80 to 120 and vice versa all the time, you`d better to keep rates on lower value.

A separate paragraph should be devoted to the quality of the servers. As i mentioned in the Lerp section, the server quality requirements will increase after altering your netsettings. When you turn rates to their max values, those requirements go even further: each FPS drop (yes, the server has FPS too) below the value of 66, even for a second, causes a lag on your screen. That`s why, before blaming my guide for not working you should make sure that the server you are playing on is good enough, and you are not playing on a laggy **** like official Valve servers.

You can change your rates by using console commands: cl_cmdrate <num> - sending and cl_updaterate <num> - receiving.

I doubt, that you understand how to set up your netsettings right after reading my guide, that`s why i prepared a few good configurations for all types of PC and internets, from the best to the worst. Start from the best, and if you meet problems (stable lags on all servers) try worse one. Remember, that in order to save these setting after next game launch, you should add them to your autoexec.cfg

Ideal

A little bit worse

Why not, if laggy otherwise

3G modem, only default settings are worse

There are some new variables that you may not know: rate and cl_interp_ratio. However, this guide is intended for players, and explaining each of these variables will not make any sense for them.