The general Quake strategy is to move around the map while controlling when, and where to get in a fight as well as how long it will last. There are two parts, the overall movement plan, and the encounters.
During an encounter there are many things to consider, one of the most important of which is weapon choice. Here's a list of weapons and the factors I take into consideration when choosing:
- Rocket Launcher; It's great for spamming places you think the enemy will be in soon. I use it when it's obvious what the enemies next move will be, and when the enemy has a small movement range available.
- Railgun; Used in long range fights or when the enemy is running away. Excellent for sniping the enemy if he has no clue where you are. Good for finishing of an enemy, deals high damage.
- Machine Gun; Useless in Clan Arena, designed as a basic weapon if there are no others available.
- Plasma Gun; Good for obscuring the enemies vision or for spamming dorways he will appear in.
- Lightning Gun; Good in medium range fights when the enemies movement is easy to trace, for example if he is falling or jumping towards you.
- Shotgun; Extremely good at finishing of an enemy or at close range.
- Grenade Launcher; Good for spamming small doorways, good for protecting your back and making sure no one follows you.
- Gauntlet; Good for Humiliating someone =p
The General Movement is the other important thing. Here's a map I made of one of the countless well played Clan Arena Maps:
(click for larger/clearer image with white background)
This isn't a blueprint and the lines don't represent how long it takes to get from one node to another. The map shows the areas of the map I connect with one another, for example, if I'm in the Lower Central Area (1) I think I could rocket jump into the intersection, teleport to Central Area (2), take the sneaky waterway to another teleporter, or simply walk the normal path. Directly after that comes the thought of where I will land. If I think about rocket jumping to the intersection, I will likely consider another route if I know that 80% of my enemies are camping in the Stairwell. Another thing I take into consideration is the tactical advantage I will end up in, for example taking the sneaky Tunnel from the Stairway to the Central Area (2) will put me on the bottom floor in a long narrow area where I can easily be disposed of. I mainly decide on such sneaky routes if I know my enemy is sitting with his back to the exit. The final thing I worry about is the route itself, for example the teleports are very loud and my enemy will know where I have gone. The rocket-jumps and waterways make a sound but only if the enemy is close by. Sometimes you can mislead your enemy by teleporting and then hiding, and sometimes he will just shoot you down. Another important factor is the length of time it would take to go that way, for example it may be useless to run around for 5 minutes if your enemy can simply turn around and shoot you in the face.
It's debatable whether predicting the other players movement is a skill that does or doesn't require intelligence, so I'm not including that here. Remember this is a very narrow window into Quake Live (... or 3), there are 5 game modes, countless items, more than 20 maps, and many more factors you will find out if you go play some Quake Live =D