I'm new to this game too (and haven't played much RTS before either). After playing through the tutorials, I'd start with a small scenario with one or maybe two AI opponents on easy. That way, you (hopefully) won't have to many ships or planets to manage at first. Then just keep building different ships and structures, trying to find out what they're good for, fend off enemy attacks and as soon as you have a decent fleet together, try to initiate some of your own.

BTW I think the user interface of this game is excellent, you can get practically all the information you need just by mousing over stuff

There've been some good suggestions already. I'll definitely echo doing the tutorials, and then starting on a small map with 1 or 2 easy AI. I would also disable pirates, a lot of new players find it too stressful/hard when they're trying to learn how to play the game and have to worry about attacks from both AI and pirates.

The basic management can be explained somewhat simply:

Planets make money. They have asteroids around them for ore and crystal. Ore is a primary building material, crystal is a primary research material (in general). You can build everything by selecting the planet. Each planet spawns its own construction ships that you don't need to worry about controlling, just select the buildings, place them in the grav well, and it'll do the rest.

Planets also have upgrades. Very important is the infrastructure/population upgrade. All new colonies start with a negative credit income (they drain the amount of credits you make) because they're underdeveloped. Upgrade their population as soon as possible (as a rule of thumb, I never colonize unless I can afford to bring them out of the negative immediately). You can also upgrade their HP (to survive bombing longer), logistic/tactical slots (for more buildings in their grav wells), and explore them to find hidden bonuses and artifacts.