The only time I've ever seen a Radio Shack that didn't sell wire was a little crappy one in the mall that mostly just sold cell-phones. Oh Radio Shack...you used to be so cool...
Anyway, to wire up your own string, you just join them together in series, using bits of printed circuit board and varying lengths of wire as needed. This means that one prong of each LED is joined to the opposite prong of another LED (more on which prong is which below). Then you throw a power supply, a resistor, and a switch into the circuit. It doesn't matter where, so long as they are on one end of your LED string or the other.
To calculate what resistor you need, you get the voltage drop and maximum current specs for your LEDs. Assuming they're all the same type (which makes the math much easier) the total voltage drop for LEDs in series is n*V. So for example, 8 1V LEDs have a voltage drop of 8V.
Then you select a power supply with a voltage equal or greater than this voltage drop. So, continuing the example, lets say we go with a battery box that holds 6 AAs. 6*1.5v = 9V.
Then you figure out what size resistor you need. The formula for this is
R = (V_powerSupply - V_drop) / I
where 'I' is the max current (in amps) of the LEDs according to the LED spec (that's the part where using all the same type of LED comes in handy).
So let's say your LEDs are rated at 75mA:
R = (9V -8V)/.075A = 1V/.075A = 13.3Ohms.
Then you pick the nearest resistor available to that value (since there's a little leeway).
In this case, it'd a 12 Ohm resistor.
When you hook up the battery supply, make sure it's in the correct direction. the '+' end of the battery supply should link to the '-' (cathode) end of the LED chain. On loose LEDs, the cathode prong is usually shorter, and the anode is longer. Sometimes the cathode prong will have a flat side, while the anode prong will be round. With the LEDs that come with their own housing, '+' and '-' symbols will pretty much always be clearly marked.
Just post a followup question here and we can check your math and sanity-check your product choices before you make a purchase.