I separate the batter into 2/3 and 1/3. Then I "color" the 1/3 with chocolate. This is for chocolate and vanilla marbling. If I'm doing more colors then I just divide the batter somewhat evenly among the colors I'll be using.
Then it's just a matter of pouring a bit of the vanilla batter then taking some chocolate batter with a spoon and letting it fall over the vanilla as I swirl the spoon around. Then I keep layering chocolate and vanilla.
When I use different colors I use the spoon/swirl technique with the 1st color without covering the bottom of the pan, then I keep alternating colors filling in gaps as I go.
A "tiedye" technique I also like is to pour the colors in "strips" and then using a knife to cut through perpendicular into each other.
Not sure if I explained myself well.