If you can, go in blind. Figuring stuff out for yourself is so much more rewarding (imo).

Try not to fast travel too much, you'll find so much more cool stuff this way.

Talk to every npc you can, they most likely have a quest for you and if not they'll have some lore expanding dialogue or just idle chatter for immersion.

Don't try do every skill tree at once. Pick a few and level them up, otherwise you'll find your skills spread too thin. A build is concrete either, don't be afraid to experiment around with the perk trees.

And lastly, just take it in. Don't try rush to beat it or stress about grinding. Just enjoy it. Playing Skyrim for the first time is a fantastic experience, so really don't feel any obligations just go at your own pace and have fun.