Plain vanilla cross-ups are pretty difficult in this game for a lot of characters, especially those that used to cross-up at will with their mediums. Most characters don’t have great normal jump cross-up options, but a couple that do are Spider-man and Wolverine off the top of my head. Also, certain characters are just easier to cross up-- Sent for example. Other characters are hard to cross up, like Commando.
Most of the cross-ups you will see take advantage of super-jump state. For ex, when Mag super-jumps and cancels the upward momentum with an air-dash forward or down-forward, the super-jump state will cause him to turn around midair before landing. If you try the same thing with a normal jump to start, you’ll notice that Mag doesn’t turn around in mid-air.
For the most part, if your character doesn’t have an air dash, you’ll want to use a decent projectile or similar assist like Storm horizontal Typhoon, or Doom Rocks, or Sent Drones to cause enough stun to let you go for a cross-up.
As for assists, the biggest thing to learn, and definitely the hardest to teach is the idea of momentum and rhythm as it applies to assists. Timing isn’t so much the right word, but pacing fits perfectly. During the course of the match you can’t just spam a particular assist-- good players are going to punish that at the first opportunity-- you have to use assists situationally. In a lot of cases, assist use boils down to one player gaining the upper hand with a good counter-call or simply a well-placed assist, followed by a series or rush attacks, where the defending player must weather the storm and turn the tables with a counter-call of his own or some sort of escape tactic that resets the balance.
Each assist works different ways for different characters. CapCom AA is primarily a defensive measure for Storm, but with Sentinel it takes on an offensive dimension. Psylocke is the basis of Magneto and Storm’s rushdown, but sometimes you just have to mash on it to use Psy to trade with certain things. By and large, the logic behind assist choice is either A.] based on making up for a weakness in the point character and/or B.] selected in order to help take advantage of the point character’s staple offense.