It's not really my first project
Okay, fair enough. You can set the X and Y positions of a sprite like you would in any other game maker or programming language. They're basic actions.
You can test for overlap with the Overlap condition so you can push your player out of solids with a loop. And you can use a private variable that changes acceleration value over time to add or subtract how many pixels per cycle you should be moving your player sprite when jumping. And since you've made other projects before, I'm sure you'll have no problem translating that knowledge to Construct once you're more familiar with the interface. The methods and practices in Construct aren't any different than other game making tools... it's just a difference in "syntax," so to speak.
And though hero_bash might sound a little blunt, he's right... if you can't work out how to make a simple jump, then whatever else you need to do that "is going to be really hard to do using the built in behavior" is going to be a little out of your league at the moment.
I would recommend taking some tutorials and looking through other people's work in the uploads section so you can get a feel for the differences between Construct and whatever other environment it is that you're used to. Make some small games and experiments. Then go tackling your own custom engine if you want.
And when that time comes, you'll get a lot more help by posting your work and asking specific questions about what's wrong, rather than just asking general theory questions with no work to show.