Most of the same fundamentals apply. Why i say most because one can take a risk a try an early mate threat that may lead to mate or win material.
What they have in common. Develop your pieces and rapidly and effectively(people forget this part). By this place them where they are the most active. Look for pieces, squares(outpost to use or take away from opponent), lines (files, diagonals and ranks) to use now or in the future. Tactics they usual tactics are always in play like pins and forks but they are not the only tactics to concentrate on in the game.
Pawns, pawns and pawns. In Chess 960 you have to extra careful with them as pieces are not where you used to them being so they can not be protected as easily. Example moving a pawn out may get it attacked and leaving you to move another pawn to protect it. By moving the 2nd pawns out you exposed a serious weakness and now stuck between giving up the pawn or leaving yourself exposed to attack. So look twice before you move a pawn as the best way for it to be defended is by another pawn. The key is will the pawn defending the other pawn create a chance for your opponent to attack.
King safety! Gotta castle. This is a long subject and not sure if it can be explained without confusion. But make sure you do not castle into trouble. Or make sure your opponent is not waiting for you to castle to side they are planning to attack. In Chess 960 sometimes keeping the King in the Middle might be safer as your opponent has no idea which side your castling and so they have they can not settle on a plan. If the center is occupied with pawns then the king is safe in the center if not then i suggest you castle.
Castle. How? Chess.com has a section on how to play chess(rules) and they include Chess 960. The will make this as easy as possible. The final positions on the king side castle ( o-o) final position is the same in both and the queen side castle ( o-o-o) final position is the same. Just have to clear the pieces out the way of the king. Remember of the King as it moves.
That is the basics!
how to play chess 960