Do what I did -- take your new bike pump to the bike shop and ask them to help you. I felt like an idiot but they were patient and helpful. The bike shop people realize quickly that I'll be back later to buy more gear from them (cycling gloves, etc., etc.). It's not just good business for them (at the bike shop, not a big chain store like Dicks), it's almost a religion. They want more people to be cyclists just like them, and are eager to get you going. At this point I can't tell you what kind of valve I have without describing it (it has a little scew thingy on the tip), but I can inflate my tires to 100 psi prior to a race.

The tire should have a max inflation rating stamped on the side so you should inflate it to that number or slightly below.

Yes that bike pump should attach to the frame. I have a pump like it and it attaches to the frame. It does not have a gauge on it though to measure tire pressure. I bought a 30 dollar floor pump that stays in the garage. It has a gauge on it. Most bike tires will have recommended tire pressure stamped right on the side of them. Most road bikes use the small presta valve, also called a French valve. Most road bikes have a recommended pressure of 100 - 130 pounds with the most common being 120 pounds. A few pounds more or less than that is ok. Mountain bikes use the fatter American valve and are more like 80 pounds pressure. Presta valves you have to take off the cap and then spin the little brass knob up to the top before you can add air. When done spin the brass valve back down. You don't spin the knob, you don't wind up with air inside the tire. Many bike pumps will have one side for presta and one side for the fat valve. You can also buy bike pumps that use CO2 canisters. Buy the pump at the bike shop, and get the one without threads. Buy the canisters much more cheaply at Wal Mart. Usually where they sell the BB Guns. But the canister is usually a use it once and its done. The pump pokes a hole in the canister and all the co2 comes out. Its much faster than than a hand pump, but if you make a mistake its gone. Most cyclists carry a couple of canisters, in case they screw up using the first one.