Here's an example of how a Snake Draft works:
Let's say you have 10 fantasy players in your snake draft, so the 1st round of picks go in order starting from 1-10. You got lucky and received the #1 overall pick in the snake draft which means you have first crack at any player you want once the draft begins in round one. You draft your player and the picks carry on until you get to the very last team in the 10th spot. Once that pick is in Round 2 will begin. Team #10 will now have the 11th pick (or 1st pick of round 2) and you will have to wait till pick #20 to make your 2nd player selection.
So to recap the team that picks 10th, will have the very next pick and select 11th. This reverse order continues till you get to the team that selected 1st in the last round and now has the 20th pick in the second round. This process continues up and down (like going from the head of the snake to the tail and then back up) until all players have been drafted.
Here is a Snake Draft Cheat Sheet you can use as a reference come draft day. This based on a 10 team league but gives you an idea of which picks each team would potentially have.