I try to use the perfboard that is pre-printed with copper on one side in the same kind of strips as a solderless breadboard. Then half the connections are made by just putting the components in the right places. For the rest, I run wires (solid core shielded, just like on breadboard) on the TOP of the board, just like the components.
For regular perf its a little nastier. I have the most luck using the legs of the components themselves to make connections. Stick a resistor in, then bend the legs until they reach the component you need to connect it to. Solder that. If you like, you can use the strippers to take a length of insulation off some solid core wire, and slip that over the resistor's exposed leads.