It's a good idea to check the part for correct alignment after soldering one pin. The above link also has some galleries of good and bad joints. It should form a smooth ramp and feather out across the pad. With either type, the solder should cling to or wet the surfaces, and not just sit on top of them. Lead-free joints will have a duller surface finish, but still be perfectly fine joints. Usually people say that joints should come out looking shiny, but this is only true for lead-based solder.
A video is available with many more details. It should spread out towards the iron tip and heat. Do this by either melting a small amount of solder on the tip before soldering ("tinning" the tip) or adding some solder at the junction between tip and work. You need to have a little solder, called a heat bridge, between the iron tip and parts. The catch is that a dry tip will not transfer heat very well.
You've probably heard that solder should melted on the parts and not the iron tip. Pink Erasor: (not shown) A pink eraser can be used to rub off oxides from older components and boards without risking damage to the parts. This is very useful for making sure parts are connected or disconnected when there're a lot of wires and parts. Multimeter: Some multimeters have a continuity check that beeps if there is a complete circuit. The sucker is a spring loaded tube that vacuums out solder and the wick is a fine braid of flux coated copper that soaks up solder. Solder Sucker and Solder Wick: Both are inexpensive ways to remove solder. Clamps: Oftentimes just resting your board on a table will be fine, but the clamps are especially helpful when desoldering parts or soldering wires together.
Flush Cutters: Used to trim leads close to the board after soldering. Wire Strippers: Two types are shown: the yellow ones can be adjusted to strip any size wire (good for small 28-30 AWG ribbon cable wires) whereas the red handled ones have several fixed hole sizes. Needle Nose Pliers: Useful for pre-bending leads, pulling out components during de-soldering, and a lot of other things. Lead-free solder melts at a higher temperature, and doesn't wet or spread out as readily, so it will be slightly harder to use. Water-soluble flux is much more aggressive than rosin, and these residues must be cleaned. 031" in diameter for most through-hole components. Avoid solid wire (no flux core) and acid cored solder (for plumbing, too aggressive for circuits). The rosin is a flux that cleans parts so solder will bond with them. Get whatever's cheaper there's unnoticeable difference in hand soldering between 63/37 and 60/40. For solder, we recommend starting out with a lead-based solder, usually called 63/37 (63% tin, 37% lead by weight) or 60/40 rosin cored solder. Not only can these be too hot, but they work by running high current through a resistive heating element, and this could apply dangerous voltages to your circuit. Avoid "solder guns" as these are meant for pipe soldering. How temperature relates to wattage depends a lot on the iron (watch a video testing the temperature of cheap RadioShack irons), and some high wattage irons have too high of a temperature. Ideally, the temperature of you iron would be between 600-700 degrees F (for lead-free solder, 700-800 is recommended). Soldering iron and solder: Just about any 25-30 Watt soldering iron will do.