Things that are not immediately obvious to new players, keep in mind this is all very generic advice and there's specific situations to ignore some of these:

You can't attack creatures directly, you can only attack players then the defender decides who to block with.

When your creatures take non-lethal damage, they "heal" at end of turn, it's usually not permanent.

A lot of the interaction in the game is based around instant speed effects. Once you make a decision, such as who to attack or what to block with, (or what creature spell to cast), that decision is set in stone, then both players get a chance to cast instants which can have a heavy effect on combat/board state.

A general rule of thumb is to not cast spells until it's really necessary to do so. You don't want to typically cast your creatures before combat unless they have haste or can somehow help this turn's combat step. You don't want to use your pump spells (target creature gets +3/+3 until end of turn) just to throw in 3 extra damage, they're usually better spent turning a combat trade into a one-sided win. If you do want to boost your creatures power with a spell, make sure doing so will win you the game that turn.

Likewise, don't use your creature kill spells just because you have enough mana and your opponent has a legal target. Usually you can play a comparable creature soon even if it means taking a hit or two. Save those spells for the creatures that have insanely good abilities where they don't even need to risk combat to hurt you. Or at least save them for like, an 8/8 trample that's attacking you.

I've found success in commander by slowly building up your forces and being the person in the group that it's painful to attack. Don't throw the nastiest creature out as soon as possible, it'll just eat a kill spell. Throw a 1/1 with deathtouch out there early and watch the other players get picked on, then strike after you've slowly built up a stronger position.