Participating with "flight following"
You can request Flight Following at anytime.

Personally, I wouldn't be in a hurry to request it as soon as you depart. Wait until you're established on course, in a cruise-attitude (instead of a climb), and everything is settled and running smoothly. Then know your position, and how you're going to report it. Know where you're going (both by name and ICAO identifier), and try to anticipate any questions they might ask.

Look for the Center/Approach/Depature where you are (look in your chart supplement for an airport close to you), and call up with:

You: "Seattle Center; November 12345: VFR, with request"
translation: Calling Seattle Center, this is N12345. I'm VFR (so you haven't heard from me before... don't be surprised!), and I have a request.

Center: "November 12345: Say request."

You: "November 12345 is SkyHawk, 10 mi. South of Harvey Field, 4,500 feet. Request VFR Flight Following to Friday Harbor"
translation: I'm a Cessna Skyhawk, my location and altitude will help you find me. I'm asking for FF to this other airport."

Center: "N345: Squawk 4532 and Ident."

You: (Set your transponder to 4532, press the Identify Button), and say "4532 and Ident, N345"

Center: "N345: Radar Contact, 11 mi. south of Sierra Four Tree, at 4,500. Traffic at your 1o'clock, 5 mi. North Bound, Altitude indicates 3,000."translation: I found you on my radar scope, and am describing the position I see you. (If you disagree, speak up!). You have traffic ahead and slightly to your right. Their transponder indicates 3,000 feet, but I cannot independently verify that.