so from what i understand. right now there isn't much of a end goal currently. you just try to maybe get all of the mons, collecting enough experience points in all the categories for all of the perks at once, and maybe try and go for the strongest mons you can via continuous breeding. 

as far as controls go, they are displayed on the main menu before you start a run, and you can check the guide for a basic idea on stuff like the basic lore and what to expect of the game, as well as all of the type advantages in the game. 

to find and get new mons. go walk around in any patch of tall grass until you get into a battle, then just defeat the mon, when the battle is won you'll get a choice to choose one of the unevolved mons from the encounter to join your team, or stable if full .  you can also get a Mon if they end up successfully breeding your scout in battle, but just know that you won't be able to use that scout again unless you give them a Salt when they are not in the process of having an egg. 

different patches of grass in the same area may still have different encounters. like for example the patch of grass next to the base at the starting spawn has lots of easy encounters to build yourself up. meanwhile the grass near the river will give you water type encounters, and the grass at the small hill of the meadow has entirely different encounters than everything else. 

the main way to get items is by getting them from stumps. just go up to them and press the interact key {R by Default}. this also applies to some crates, chests, and rocks with evolution stones. a secondary way to get items even after everything is collected is from the two perks that give you items upon releasing and sending a mon back into the wild.  {the higher cost perk gives you a better chance of getting rare items when releasing, and having both gives you the best chance of rarer items when releasing.}

to evolve your mons you Have, yes HAVE, to give the mon you want to evolve the appropriate evolution stone for their type, or a universal stone. there is currently no other way to evolve mons as of writing this.

breeding is something that currently you can't really do until you have already lost a scout.  but there is plans to have it be done with enemy scouts as well.  in order to breed and get eggs, you go to the stable in the menu and you select which ever scout is currently available, then you select a mon to pen with them. after they are penned in you select join and bam, now that scout is pregnant and you just have to wait a few days for them to produce an egg, then another few more days for the egg to hatch.

there's a whole lot more to go over like food, camping, and what not. but ill leave the rest for you to figure out. hope this at least helps!

and feel free to ask me any other questions, been following this game for a long while now. :)