How soon should I start tanning before vacation?

I'm going on vacation to Hilton Head in the beginning of June. I live in Ohio so it's still chilly and I'm pretty white. I want to go tanning before so that I don't burn the first day there and ruin my whole vacation. I'm blonde with blue eyes so I want to get a good base tan before I go. How early should I start going tanning and how long should I stay in the beds?