You don't necessarily HAVE to install the LEDs on a piece of perfboard (perforated prototyping circuit board, like
these). You could use a rigid piece of material, like thick cardboard or thin plywood/veneer, as the mounting surface for the parts. You would use a template of some kind (maybe the dot-matrix pattern suggested earlier), and draw the characters onto the board. That way, you can see exactly how the LEDs will look (draw small circles where the LEDs will stick through). Once you have the character and hole locations defined/drawn, use a drill bit that is big enough for the shell of the LED, but smaller than the ridged "collar" at the base of the LED (most round LEDs have a raised ridge on them). Determine the size by drilling a few test holes in a scrap piece of board. Dry-fit the LED into the holes, and find the best fit.
Once you know the hole size, and locations, it's time to drill the holes out. Once the holes are clear, you need to plan on LED location, orientation, and connections. Draw a scale layout of the board (put a piece of paper under the board, and use a pencil/pen to mark through the holes, onto the paper.. now you have an exact copy). You'll want to run 3 LEDs in series, and connect each set of three to a resistor, then back to the power source. Using your paper template, start penciling in which LEDs you'll wire together in sets of 3. The ends of each set (plus their resistors), will be connected together, run through a switch, and connected to the power supply. Like this (ignore the leading periods, the are just spacers):
Supply+...........................................................Supply -
..........|-- LED1 ---- LED2 ---- LED3 ---- Resistor --|
..........|-- LED1 ---- LED2 ---- LED3 ---- Resistor --|
..........|-- LED1 ---- LED2 ---- LED3 ---- Resistor --|
..........|-- LED1 ---- LED2 ---- LED3 ---- Resistor --|
..........|-- LED1 ---- LED2 ---- LED3 ---- Resistor --|
Once you have a wiring plan established, and have determined a suitable power supply (and associated resistor value), you can start installing the LEDs and wiring them up. Anode = + terminal, Cathode = - terminal. Connect the power supply to a switch (if desired), then the switch to the anode of the first LED(s). LED1 cathode to LED2 anode, LED2 cathode to LED3 anode, LED3 cathode to bias resistor, bias resistor to ground lead (power supply - terminal).
Put the LEDs in the holes. If they fit snugly, then you may not need to tack them in place (so they don't move while bending leads and soldering. If they want to move, use a hot glue gun to put a spot of hot glue on the back of the LED, to secure it to the board. Bend the leads, trim them, solder them, and test one set of LEDs out before doing the rest!! Route the power wires around cleanly. Use zip-ties to bundle them together, and then a blob of hot glue to tack the bundle down to the board. The best part about hot glue is that you can use the tip of the gun to warm it up, and loosen it up after it's hardened.
You could paint the board after you get it drilled, so that it's some desired color, rather than cardboard brown, or shows wood grain.
---------- Post added at 23:48 ---------- Previous post was at 23:15 ----------
Which color of LEDs did you buy? That will affect the voltage & current calculations, as well as the number of LEDs in each string (high voltage LEDs will result in fewer LEDs per string, which means more strings, more resistors, more complexity).
If you look at the table above the shipping policy, it will tell you the Typical voltage for the various color of LEDs. They show that the parts are all run at 25mA (If is that parameter, I is current, f is forward direction, so If is forward bias current). 25mA will be really bright... like mentioned before, I'd probably bias them up around 15mA.
If you use a standard 12 VDC transformer to power this rig (using Red LEDs, so 2.0V per LED)....
12V / 2V = 6 LEDs, max. However, that gives you no extra voltage drop for the bias resistor, so we use 5 LEDs per string.
5 LEDs * 2V/LED = 10 volts of drop.
12V supply - 10V across the LEDs = 2V across the bias resistor
Now we use Ohms law to figure out the resistor value. V = I*R (voltage across a resistor, volts = current through the resistor, amps * the resistance in ohms).
So 2V across the resistor, and 15 mA (0.015 Amps) through the string...
2V = 0.015A * R(ohms)..... R = 133.3333 ohms. The nearest
standard values are 120 and 150 ohms. I'd opt for the larger value. That will make the current be slightly lower than the target, but that's not all bad, since no two components (LEDs or resistors) are exactly alike.
Now to check the power dissipation of the resistor (V = voltage drop across resistor).
Power = V*I = V^2/R = I^2*R
So, power dissipated by the resistor will be:
P = V^2/R = 2^2 / 150 = 0.027 watts. If you use a standard 1/4W carbon leaded resistor... 0.25W >> 0.027W, so you have lots of margin, and won't be prone to burn up resistors.
Hope that gives you the tools/equations to calculate the number of LEDs in a string, when you determine your power supply, and how to figure out the bias resistor value.