To play Slither you need two players and a graph. Each player has a different color to mark the graph. The first player picks a vertex of the graph and marks it with his/her color. Then players take turns picking vertices which are adjacent to the last vertex picked. (That is, they have an edge joining the vertices.) This is marked by coloring the new vertex and the edge between the last vertex and the new vertex. The last person who is able to pick a vertex is the winner.
Try playing on several different boards. Keep track of whether the first or second player wins and see if you can find some strategies to help you win! After you have played a few games, you can click here for a hint.