It's hard for folks to show you what they've learned over the years, but you've gotten some good advice here. Dolphin are great fish to target when you're new to offshore fishing -- you don't need a lot of expensive equipment and when you find the fish, they usually are agressive and will hit almost anything.
Simple tackle will work fine. For trolling, 20lb and 30lb gear spooled with mono will work fine. Reels such as the Penn 113H, 45GLS (no longer in production, but a great 20/30lb trolling reel), Shimano TLD 20 and 25's are all great for trolling. For spinning, 15lb gear is fine. Penn 650's are perfect. For trolling rods, 6'6" long rods rated for 20-40lbs and ring guides are fine. For spinning, 7' rods rated for 15-25lbs.
Leaders. 80lbs mono is fine from my experience -- though some folks like heavier stuff. The nice thing about 80lbs is that you can still tie knots -- once you get to 100lbs mono, you should go with crimps.
Terminal tackle. When trolling, make sure you DON'T use barrel snap swivels -- use the more expensive ball bearing snap swivels. Under the pressure of trolling, barrel snaps won't spin and the line will twist, the ball bearing ones will make sure things swivel properly.
Hooks. Match the hooks to the lure/bait you're using, not the fish you hope to catch. 5/0 to 7/0 hooks should be fine for any trolling lures you'll use.
Lures. Lots of personal preferences in this area. No need to spend a fortune. Moldcraft lures are excellent. Try their Super Chugger (small size), Hooker, and small Wide Range rigged with 6/0 or 7/0 hooks. Here in Florida, no captain leaves the dock to target dolphin without a blue and white Iland Lure -- they are that good!!!

Rig them over a medium ballyhoo and hang on!. My other "go to" dolphin lure is a Mini Green Machine.
I'm assuming you have four rod holders in the gunnwales. The two furthest aft should be pointing straight back. They are your "Flat Lines". You'll run those straight back on plain lures, say a Wide Range on the starboard and a Mini Green Machine on the portside. Place one 20-30' back and the other 10' further back from the first.
The next two rodholders should be angle out at approximately a 45 degree angle. You can run ballyhoo off these, either "naked" or with "skirts" over them.
Finally, I'd reccommend you buying a DVD or two that will go into great detail on tackle, bait rigging & fishing for dolphin. George Poveromo has two: They are, "Dolphin" and "Offshore Bait Rigging". Both are well worth the $$.
http://georgepoveromo.com/showstore.htm#Bait
Here are some other tips:
http://www.saltwatersportsman.com/ar...sp?ID=21013128 http://www.saltwatersportsman.com/ar...sp?ID=21012616
Tightlines!
PB