This is what I've learned after a few hours of Urban Terror game-play, in TDM (or Team DM, Team Deathmatch) mode, and considering myself as being novice in UrT. The hints apply mostly to all fast-paced arena-style FPS, which prefer fun over realism.
1. Go for action. Tactics over strategy. Avoid being "smart" and creeping up on your enemies in assassination mode. While this may work on the Riyadh map (see all standard maps here) it requires trained precision and knowing the not so obvious sniper hide-outs. And it requires sheepish enemies who can't turn your camping on you.
2. Decide if a map needs brute force or precision at a distance. Some maps can be played both ways. For brute force, select the LR300 and extra ammo + protective gear. For precision select the G36 for sniping from a distance, while you can switch into mild brute force attack at times.
3. Game the engine. As it seems, at least in UrT, friendly fire does not hurt your team. So when your team is in a brawl with the enemy, join in. This works especially well with brute force. For example, use the LR300 on auto-fire while standing a few steps behind your team, and engage on a group of the other team - as heavy back up of sorts.
4. Aim high. The days of game engines differentiating between hitting and not hitting at all are over since, well, forever. Contemporary shooter engines differentiate between a hit on the head, the body or limbs. So try to go for the "expensive hits" as they will take out an opponent much quicker. You can inflict immediate 100% damage with one well-placed virtual bullet.
5. Learn from the best. Use spectator mode to see what the good players are doing - by "following" - and learning from them.
5a. Learn from which weapons other players are using on a specific map.
6. Most default maps, at least Abbey, Casa, Sanctuary, Algiers, Tunrpike / Piketurn, Austria, Subway, have one (or two) "culmination points" where the teams usually clash. (You'll learn where these are after a few turns on a map.) Alternate between "straightly going there and joining the action" (brute force, mostly), and then "sneaking around the other path" to join the same action from a different angle (more in precision mode) or putting your efforts into the "tier-2 culmination" point. Just for a change.
6a. Note that you can switch weaponry and equipment between spawns, sometimes - as it seems - you can even do so shortly after spawning.
7. Experiment with weapon and equiments slots. Having no secondary weapon, or less heavy equiment may enable you to carry a third or fourth equipment item. You may wish to carry only one weapon and protect yourself heavily, or you may trade weapons and ammo for less protection. Also note that you can drop and pick-up weapons and ammo during a round on the map.
What's Urban Terror?
For the casual gamer, on Linux, there are two (major) First-persons-shooters available for free: Xonotic and Urban Terror. The first is a Quake III Arena Engine based free Quake III alternative with an improved/updated codebase and the latter, UrT, the same, mostly, a total conversion of Quake 3. Xonotic goes for the unrealistic/sci-fi "batttle in space" look, while UrT is more realistic and a depiction of urban warfare. As of this writing, UrT seems to be the more active one.
Please remember: Gaming is fun, be nice. FPS style games are a game of skill! Not reality. Play fair, be nice, and after a fast-paced round of gaming, act peaceful and respectful in real life.