Skyrim is a lot of fun, definitely a non linear sandbox type RPG where you can explore and do quests to your heart's content.
In terms of levelling, your skills level up automatically as you use them. Pretty simple. Each time you level up a skill, you gain XP towards an overall character level. When that happens, you gain a perk which you can put in any of the many skill trees (constellations) if you have the base level requirement for it. When you level up you also get to choose to get an increase of health, stamina, or magicka.
Unless you plan to be a mage character from the start, I wouldn't invest in magicka until much later in the game (maybe level 40 or so). If you're a melee character, focus on levelling up with health and stamina.
As far as perks go, put them into skills that will benefit your playstyle. Using a one handed weapon and a shield? Invest points there. Using a two handed weapon and no shield? Invest in two handed and either light or heavy armor depending on what you wear.
There are no rules to any of this. Just some suggestions. Have fun and do a lot of exploring. If you run into a quest that is giving you trouble (enemies too powerful, etc) you can either dial down the difficulty on the spot, or, simply leave and go do some other quests, level up a bit and then go back.
Have fun!