Transistor Design ... Simple Approach
The following is a rundown of how to design simple NPN transistor circuits.
Basically, a transistor sets the Collector current (Ic) to be equal to the Base current (Ib) multiplied by the transistor's Gain "Hfe" (typically around 100). [IC = Ib*Hfe]
This lets you turn a large device (such as a motor or a Laser) from a small signal (such as from a microcontroller or a sensor). However, the transistor also requires a voltage Vbe between its Base and Emitter (typically around 0.7V). Here is an example circuit:
1st step is to determine how much current & power your load will take. If the load is a Laser or a Relay, then it should only be about 100mA at 5 or 12V, which is upto 1.2Watts (Power = Volts * Current).
2nd step is to determine the maximum Base current (Ib) you will have. If the Base resistor (Rb) is connected to a microcontroller, then this is generally a maximum of 20mA (enough to power a simple LED but not much more).
From these 2 steps you should find a transistor that has Max Collector Current (Ic) and Max Power Dissipation (Pd) ratings that are atleast twice your requirements (for safety), and has a DC Gain (Hfe) large enough to convert your Ib into your Ic. To amplify small signals or to turn on a small Relay / Motor / Laser under 100mA using a microcontroller, use a small transistor (eg: BC548) in the TO-92 package, but for any larger currents or power you will need a larger transistor (eg: TO-220 package), possibly with a metal heatsink.
3rd step is to determine the Base resistor value (Rb) to give the correct voltage Vbe (typically around 0.7V) for the transistor, based on what you are connecting it to. Use Ohm's Law (V=I*R) to work out the resistor that would give you the desired current (Ib) between the resistor's voltages (Vin and Vbe). Ideally, Ic = Hfe * Ib = Hfe * (Vin - Vbe) / Rb. However, transistors aren't perfectly linear amplifiers, so you wont get quite this much current output.
When you are trying to either switch something to be completely ON or completely OFF (which is a good idea for Relays, Lasers and Motor PWM), then you want to use the transistor at its "Saturation" limits, which means making Ib about twice as much as you originally calculated, so that it is definitely ON or OFF. In these cases, you can think of the transistor as a switch, that is open (not letting any current through, therefore Vce = Vcc) when Ib = 0, and closed (letting all the current through, therefore Vce = 0 or 'short circuit') when Ib = max. Just be aware that even when you have saturated the transistor on (Ib is max), Vce wont actually reach 0volts, but will usually be between 0.2 - 0.7V depending on the transistor.