In addition to the perfboard and a soldering iron, you'll need some fairly common tools and supplies:
Kynar wire: This is an insulated 30-gauge single strand wire. It's a rather thin wire which is useful for low current and low voltage digital circuit connections. I use three colors: Blue for Ground, Red for +, and Orange or Yellow for all the other connections. This wire is also "pre-tinned" so it takes solder very easily.
Wire Cutter, Wire Stripper and Needlenose Pliers: I have a special stripper that is permanently set to strip the Kynar wire. It may take a few tries getting the correct setting, since you don't want the stripper so tight as to nick the wire itself, or so loose that it just slides off of the insulation. A good pair of needlenose pliers are required to hold short lengths of wire when stripping off an end.
0.8mm Rosin Core Solder and Solder Paste: The paste (you can use a rosin pen as an alternative) is useful if you want to flow solder over and join a socket pin, a wire and copper pad quickly and without too much heat.
Tweezers: I have a surgeon's tweezer (the kind you got in biology class in school when you had to dissect that frog) that I use for looping wire ends and a sharper, more precise steel electronics tweezer for holding wire during soldering.
“Helping Hands”: This inexpensive reconfigurable alligator-clip holding device is an indispensable tool when using this prototyping technique.
Reading Glasses / Magnifying Glass / Manual Dexterity: Depending on your age, reading glasses may be of assistance. If you don't have steady hands, you may have difficulty managing some of the smaller, more finicky aspects of this technique. If that's the case, printed circuit boards are probably a better choice.