After playing Quake Live I noticed how the the max fps you can get is 125. Normally the max you can get is 60, but after playing Quake I decided that I want to get 125 on all my old games. I'm not that much of a tech guy but could someone give me some instructions on how to achieve this?

You'd usually accomplish that by disabling vsync and removing any framerate cap set by the game itself. How to do this (and whether you can do this) varies from game to game. Do bear in mind that going over 60 FPS in a game at the rendering level generally won't make a difference to actual visual quality.

First, what possible advantage is there to running a game at a higher frame rate than you can view? It's just juvenile e-peen waving.

Second, SS2's physics engine gets weird at very high frame rates, so you really don't want to do that.

It's not the visual aspect that I'm interested in, it's the smoothness of the gameplay. I know Quake is a fast pace game but running it at 125FPS is a type of fluid gameplay that I have never experienced. I've been looking around and what I have learned (so far) is that Quake was built from the ground up to run at 125FPS but most games can only max 60, after that the game starts to experience problems. My question is how does Quake accomplish this when the refresh rate on a typical computer monitor is 60.

125 FPS is the cap on the game's GPU rendering rate. You still only see 60 FPS on the monitor, assuming a typical LCD. (CRT monitors often supported slightly higher refresh rates, with 75 being common, but this was coupled with much slower response times.) You're also capped by the fact that your eyes generally can't register any real difference beyond 60 FPS (flicker generally stops being noticeable around 55 FPS).

In many cases a game can still render at a higher internal FPS, but that's not what makes the difference to gameplay smoothness - that comes from the fact that your system is powerful enough to avoid framerate loss due to bottlenecks (heavy CPU use, disk loading, etc) causing the FPS to dip below 60. (This isn't terribly surprising if you're running an old game on a modern system!)

Most games impose some sort of internal cap (120 or 125 is typical without vsync enabled; vsync means a cap of 60 with an LCD monitor) simply to avoid overtaxing the graphics card, and removing it can result in the game running at hundreds of frames per second on the GPU... which doesn't do anything for visual quality but is very likely to result in overheating or burnout of the GPU and/or power supply.

Likewise, sometimes a game's physics engine processing is also tied to framerate (and this has become much more common over time), but this usually results in problems rather than benefits if you uncap it. The intent of linking the two is that physics processing gets dialed back if the system is struggling to keep up; going over the vsync rate thus results in things being overprocessed and behaving strangely.

It's still not clear at what framerate the human eye cannot tell the difference anymore. It is possible that humans can still tell the difference between 60 FPS and 120 FPS and possibly even beyond that. Keep in mind that humans are predatory carnivores, so our eyes are quite well developed for fast movement.

Anyway, the most important thing is that the screen has a high enough refresh rate. My screen, like most LCDs, has a refresh rate of 60Hz, so even if I was able to see the difference beyond that my screen wouldn't be able to display it. Anything beyond 60FPS is basically useless for me. If your screen has the same limitations don't even worry about framerate anymore, 60 FPS is the best you can see.

Most games have an upper limit for their physics simulation, like 60 FPS, and if the framerate exceeds it the graphics can be made independent. Then the game interpolates the position of an object. in other words, if a bullet is flying from A to B within one frame of simulation, the graphics will draw the bullet between those points, but the actual bullet will still "teleport" from A to B. This creates the smooth look, without breaking physics.

The only reason you would have any use for more than 60 fps is if you spend a lot of time walking towards or jumping up and down in front of your screen. Vsync capping the fps at 60 is almost always better than the screen tearing and GPU overheating madness you get without it.

TVs and computer monitors marketing themselves with slogans like "100hz" might as well be writing "With BLAST PROCESSING!!!" all over the box.

I think the myth about excessively high FPS improving gaming performance started and died with Counter-Strike in the early 2000s. Most CS-kids turned into hypocondriacs believeing that anything less than 100fps gave them head aches and eyes strain, and that the higher the FPS the easier it was to aim and fire first. I don't know what how fast the Gold Source engine (Half-Life 1) cycles but it is probably between 40 and 80 times per second to check player input and compare positions of game entities. Unless your frame rate is dipping into big screen cinema levels, you are not missing out on anything. If the game feels sluggish at 60 fps the problem lies somewhere else, it has nothing to do with graphics rendering. I once had some spyware cause tiny delays and microstutter in Battlefield 2 and it was driving me crazy until I figured it out.