To level up, you need XP. After each level you get one skillpoint that you can spend. You have a 24hour trial period for each skill, so you can still get rid of it without penalty. If you upgrade a skill you already have (F.e: Light Turret --> Medium Turret) it will cost more than one skillpoint. (Atleast, this is how I understand it, please correct me if I'm wrong)
I think weapons are unlocked by leveling and weapon attachments by completing challenges. I'm not certain, I find it still a little vague.
You wind up with 20 skillpoints at the end of the game. There are 10 skills for each class specific tree, and therefore 10 skill points required to master one class, and 10 general purpose skills that apply to all classes. 4 Classes/Class Trees, plus one General Tree, equals 50 skills to spend skills on. Each one requires one skillpoint, so you can only buy 20 of all 50 skills. So your character can specialize in one class by getting all class specific abilities and all general abilities- thereby being the best they can possibly be at a single roll- or they can master two jobs, and therefore be really good at two classes, but not as good at one of those classes as someone who took the general abilities, or you can generalize by taking half the skills in all the classes, or semi generalize by taking half the skills in three of the classes and half of the skills in the general tree.