Do some sparring in Training mode
A great way to start things off is by doing some sparring in Training. Here, you can select any of the fighters that you've unlocked and test them out. Try out your powers, see if the character is right for you. Work on your combos and improve.
You can't really work on things like blocking, but you can get comfortable with your fighter's attacking skills. Heck, aside from that, it could be a good way to blow off some steam. Get in there and beat the tar out of your sparring partner.
Once you get to multiplayer matches, it can be unpredictable. Sometimes you may do well, sometimes you may find it frustrating. So go ahead, head into training to dish out some beatdown.
Start with Story fights
I know it's easy to jump straight into online matches once you complete the tutorial, but that may not be wise. Instead, play through the story a little bit. It is a pretty intriguing one, especially considering the background of each Skullgirl. It's also a good way to work on your craft.
The Training mode is great too, but if you want more of the real deal, then definitely try some story mode battles. You'll get challenged more, letting you hone your skills in the process. You'll get the chance to unlock some more characters too as you play. So, get that work in, dominate, and get rewarded for your efforts. All while learning more about the back story.
Work on your blocking
One of the more important things to keep in mind when playing is to block. In multiplayer, this is something that definitely can help you out. This is something that you can certainly practice in the story mode. Of course, you can't block forever, but just use it at the right times.
Then, after some good blocking, do some counter attacks and punch them in the mouth. A good block and then unleashing a nice combo is a satisfying feeling in Skullgirls. Punching is your best basic weapon, but blocking is your smartest. Use it wisely, warrior.
Use your powers
Each of the Skullgirls have their own signature powers. You can build it up by getting in some combos and dealing some damage. This will let you unleash your deadly special move. This can be immensely satisfying when you have your opponent where you want them.
Feel free to use it early, but by waiting until you get their health down a bit, you can really go in for a K.O. And not only can you unleash your haymaker, but there are also some mini-super moves that you can use repeatedly. You just have to make sure to wait until the cooldown period is over.
Punching, kicking, and blocking are the core of the action, but use those supers when available. They're deadly and their cool to look at. And these moves could play a big factor in which character you choose. You may like one fighter's supers more than others. For the ones you unlock, give them a test run and see how you like them.