It's been a while since I've seen a thread about this (forgive me if I'm wrong) and I just wanted to post a link to the local wiki page and point out a couple highlights, hopefully to get some more interest or at least awareness to one of the most distinctive features of this game. For some of you, this is common knowledge, but I didn't know about any of this for a while after I started. So for anyone that was curious:
http://wiki.spiralknights.com/Gates or type "gates" in the search bar. There is a really good article called "Spiral Knights Gate Maps and You" in the Useful links sticky up top.
You can access the gate map at any time during a level by clicking the main menu icon (looks like a gear) and selecting "Gate Map." This map shows you all the possible future depths in your current gate. You can do this during missions as well, to look ahead to see how many depths (and what type) are left in your current mission. Learning how to read and understand your Gate Map is crucial to your appreciation of the Arcade.
The Icons on the Gate Map are full of useful info, like what type (deconstruction zone, arena, etc), any status effects, prevalent monsters, Clockworks Terminals (for recipes from Basil), etc. There is also info on the rotational direction and future depths so you can wait for the depths that you want to take. If you are a new recruit, still cutting your teeth with only normal/piercing armor, why not shoot for the gates that have beast and jelly stratums when making a basil run, for example. Check the bottom of the linked wiki page for an awesome chart that breaks down the level combinations and stratum themes. It shows what every icon, icon color, background color means.
The Arcade is an interesting, semi-customizable way to farm crowns, materials, heat, and meet new people. You can choose your gate and (to an extent) the flavor of the depth you are about to descend to. If you save up minerals, you can influence the flavor of upcoming gates during gate construction. It is a big part of the game that (depending on markets of course) can offer an equally profitable (more profitable if you're lucky) alternative to the mission grind that so many people complain about. Cheers.
You can also press "M", click Arcade, and then click the gate and tier you were in, then voila! You know the possible future gates too!
Sarcasm not included.