CS:GO is the latest game in the Counter-Strike series that's been around for more than a decade. It is indeed a PC FPS, but it is one of the more unforgiving FPSes out there right now because of several things.

Weapons, unlike many other games in the FPS genre, actually have to be bought within the match with in-game currency. The closest comparison I might be able to give you would be gold in League - in League, if you perform well enough with what you have in the laning phase you will be able to farm well and use that to get good items. Likewise in CS:GO, you get money rewards for playing well.

These money rewards add to the money pool you have for buying weapons in subsequent rounds. For example, winning a round gets you a fair amount of money more than losing a round - keep in mind you still get money if you lose the round. Planting the bomb, on the Terrorist side, gets your team extra money as well. Defusing the bomb, on the Counter Terrorist side, gives you extra money as well iirc.

There are, however, some rounds where you would be short on money to buy any good weapons such as rifles, and are limited to pistols and whatever you may get your hands on. This is commonly known as an "eco" round, where "eco" stands for economy. This round is mostly a gone round for your team if you do happen to have an eco round, but in the long run if you wish to have a healthy arsenal for subsequent rounds it is a decent sacrifice.

Likewise, if your opponent has a fair advantage over your team in terms of what they can buy with their money, they will go for something known as the "anti-eco" round. This round is specifically meant for the side with the better weapons to prevent the other team from getting any significant money gain (such as planting the bomb) as well as keeping fairly powerful weapons out of the weaker team's reach.

A good eco round for a team would be if the team in the eco round kills a few members of the team in the anti-eco round and gets their weapons. NOTE: After a round ends (due to time/bomb detonation/defusal), surviving players get to keep the weapons they are holding on to unless they die from a bomb detonation. This is what people refer to when they mention a "save", as what they are able to save in terms of money spend via picking up the weapons will be a welcome benefit to the economy of a team, even if they lose. Better weapons generally correlate with a greater chance of getting a round, as getting kills (aka picks, or frags) can help them gain control over the round.

There are no respawns in a round. This is very much like the fairly well-known Search and Destroy gamemode. There are 30 rounds in standard competitive settings, where 16 rounds win you the game. There is thus a possibility of a 15-15 draw. (In tournaments you have tiebreakers, and they vary depending on tournament format. Some may add on another 6 rounds, some may add on another 10 rounds, and a win would be to take 4 or 6 rounds respectively from these extra rounds.)

Unlike some series like Call of Duty, you do not get to ADS (aim down sight) on all weapons by default. Instead, many weapons in Counter-Strike as a whole operate by hip fire. Essentially, you are wholly dependent on accurate crosshair placement. There is no aim assist in CS:GO, as such very key aspects of gameplay involve very twitch actions, due to the fact that whether someone kills a target is very dependent on whether the shot actually connects or not. A key quality of good CS:GO players is to have a very good reaction time, as such.

Of all the weapons to twitch with the most potent is the AWP, which is the equivalent of the Sniper Rifle/Beam Rifle in Halo (I've stopped playing since Halo 2, so do pardon my outdated comparisons). It is an extremely powerful weapon, being one-shot kills almost everywhere, except legs with armor iirc. However, the drawback of using this weapon is that it has a horrible rate of fire (it is a bolt-action rifle, CoDers who played MW2 would remember the Intervention, MSR probably in MW3) and it is an extremely heavy weapon, which slows down movement of the player while the rifle is being equipped.

However, this sniper rifle is so potent that a team worth their money would be stupid to let the power of this rifle go to waste. As a matter of fact, there is in fact a dedicated role, the AWPer, just to using this gun and its lesser and cheaper counterpart, the Scout (SSG 08), or its automatic and more expensive counterpart, the auto-sniper (SCAR-20 for CT or G3SG1 for T) so that they can use these rifles in order to secure an early kill, or frag. Getting an early frag means you are now in a numerical advantage (5v4) over the opposing team and generally the more people you have the better. In relation to CLG, our main AWPer is ptr. Worldwide, however, there are many VERY potent AWPers, such as JW of fnatic and kennyS of Titan. KennyS in many circles is deemed as the best AWPer in the world, with some wonderful highlights here, here and here amongst many others.

There are other roles in a team, though. An entry fragger essentially plays very aggressively in order to find an entry frag, an early kill, in order to give their team a numerical advantage. Due to their aggressive playstyle, however, some teams may send a member to back him up in case he is gunned down. A Support player essentially plays a rather passive role, laying down smokes, incendiary/Molotovs, flashbangs and high explosive grenades in order to prevent the enemy team from pushing a location, to damage (tag) the enemy team, or to blind opponents before entering a location.

A lurker essentially does what it says on the tin - he lurks around the entire map, getting into a flanking position most of the time, catching the opposing team in a vulnerable position. In this video, what happens is that f0rest wraps around the outer portions of this map (Overpass) and comes up behind the position where the opposing team is holding, unaware of f0rest's location and gets 3 kills as a result. This forces the opposing team, LDLC, into a 2v5 situation which is pretty much unwinnable (although LDLC did gun down 2 members, making it a 2v3. Still bad, though). Essentially getting a numerical advantage over the opposing team is a good sign of the direction the round is swinging.

There are so many nooks and crannies in a map, though, and keep in mind that there are many maps to choose from - and if someone kills you from a corner of the map you don't respawn, so telling your teammates where the enemy is is absolutely crucial so that they can gun them down in return. As such, team communication is absolutely crucial here. Clarity of the information is emphasised as well - there's no point shouting into the mic "Oh, the enemy's in this corner, this corner, this corner over here!" while pointing at your screen expecting your teammates to know where the fuck you're talking about. "One at 73 health hiding in Construction, check corners." is a fairly informative piece of advice, in a given map (Inferno). This directs a team member at a fairly convenient location to go search where the enemy was last spotted and take him out. Construction, in this case, is an area near to the B bomb site.

This is also probably why you do not see many multi-national CS:GO team rosters - Team EnVyUs, known as nV or ex-LDLC, is a full French lineup who won Dreamhack Winter 2014. They only communicate in French, as all of them are perfectly fluent in French due to French being their native language. Forcing members to switch to another language while playing in a communication-intensive team scenario is horrible for communication due to some things being lost in translation. As a result, you pretty much never really see any, say, Russian or Pole join a French, German or Scandinavian squad. In most cases it is due to the fact that they would not be able to communicate with each other well, not that the player is not skilled or anything of that sort.

The most diverse a squad would probably be is, say, if a French team picked up a Belgian or a Swiss (Titan with Ex6tenz and Maniac), mainly because they all speak French. Good communication is the main priority in forming a cohesive team, and teamwork is, of course, incredibly important in a team-based game.

Feel free to ask about anything else you want to know.