Seil's already covered a lot, but movement is often confusing enough to beginners that it deserves a tip of its own.

Warping to someone else's beacon is easy enough--enter cloud view, tap their beacon, and then tap the warp icon, but moving around in local view isn't as obvious. To move, you tap anything friendly, whether it be beacon, ward, catcher, gate, dominator, or even another mage, and then pull down the rune screen and draw an upside-down U (like a hop). You will warp beside whatever you tapped.

If you didn't end up in the direction you wanted to move, then just tap your target and warp to it again. And again. And again. Eventually, you will overshoot it in the right direction. When you're hopping over a friend, this is called 'leapfrogging' and is the easiest way to travel locally/go raiding in Shadow Cities. The more friends you have, the faster you can move.

When coordinating what direction you want to move in, the little arrow on your mage's circle will always point north.

Lmao how did I forget to talk about this in my thread x.x nice

I'm glad you didn't, because I started writing it before you posted yours!

Spent quite some time typing mine up too though =p