I'm not in a position to ask what order you'd prefer this in, so you're getting the bad news first. You see, as much as I love the multiplayer aspect of UT3 almost as much as I love my appendix, I find one particular aspect of the former as useless as the latter: the menu interface, especially the server browser. As if it wasn't bad enough that servers seem to pop on an off the list depending on if there's a ‘T' in the day, there's no option to connect directly to the server without using the console (and if you're thinking ‘the what' you've proved my point as to how stupid that is). This means that even if you do know that you can connect to the TrustedReviews server on the IP address 18.104.22.168:7777, there's no option on the menu to do so.
Filtering is pretty lax too; for a start it's on a separate page to the browser, which sounds reasonable, unless you know that there isn't an option to just show every server available in the world and that instead you'll find you have to choose a particular game mode within which to browse. I will concede that all of these are minor annoyances, but that doesn't make them forgivable, especially in this day and age. On the lighter side, by the time I've managed to navigate my way through the unwieldy interface and actually get onto a server, I'm just about infuriated enough to be in the mood for some killing and a small part of me can't help but think Epic purposely made the menus so bad for just that reason.
So, you finally get on to a server without throwing your mouse out the window, what next? Well, that would depend on what game mode you chose and on that basis I guess I'd better explain what said modes are. Starting with the old-school UT originals, we find the classic all versus all Deathmatch, the almost-as-classic Team Deathmatch and the not-all-that-classic-but-still-brilliant Capture the Flag game types - pretty self explanatory. The latter also comes in a second variety that adds vehicles to the mix, more on which later, and to my mind is probably the second best game mode.
The best mode, if you want my opinion, by far has to be Warfare. Building on the Assault and Onslaught modes from UT and UT2K4 (and sadly omitted from 2003) the basic premise is fairly simple, but it leads to some complex strategy. Warfare maps are interspersed with various capture points, called nodes, which are lined together and must be captured in order until you have a direct path from your base to the enemy's, whereupon you rain destruction on their reactor core casing an explosion and winning the round. Last we find Duel mode, a winner stays on one versus one battle to survive. The twist, if it can be called that, is that the winner also gets to keep armour and weapons form the previous round giving them the advantage over the newly spawned opponent. While duelling is fun for a few minutes, I personally found it got old pretty quickly; at the end of the day UT is not a two player game.
It's all well and good knowing why we're killing each other (aside from the fun of it) but we still don't know how. Luckily, that's an easy question to answer: guns, lots of them, and big ones at that.