Mass Effect Andromeda is, regardless of how slick its combat might be, an RPG. As an RPG, it expects you, as the player, to make some choices about how the characters you play as will develop. The central mechanic in the game is levelling- like with all RPGs, you gain more XP the more you interact with the world, and once you have enough XP, you gain a level.
When you gain a level, the game prompts you on screen (and this is your cue to go into the levelling screen). In the levelling screen, you use Skill Points you get awarded upon levelling up, and allocate them across various parameters, which govern your Offence and Defence, among other things.
A final thing to keep in mind is that your squad mates also get XP and also level up- and they don’t do this automatically. You need to go into their levelling screens and allocate Skill Points for them, too. It’s for the best, really- it means every character will end up playing exactly as you want and need them to.
One fastest way to unlock skills and earn experience points is to do side missions (besides completing the main missions). Certain side missions are dynamic and will only show if you explore enough. In the very first mission, there are like 5-6 optional missions which will only show up if you explore the area completely. As you are a Pathfinder, exploration is the key towards faster levelling up.