Batteries and controls

The motor is obviously a key component, but you need a battery to supply electrical power and some controls to make everything work together.

The capacity of battery packs is given in watt-hours (Wh), which tells you how much power in watts can be delivered for how long.
A 500Wh battery pack should in theory be able to run a motor flat out at 250W for two hours (less a bit for efficiency losses). In practice the motor is usually running at lower power so you'll get longer, although also it's not a good idea to fully drain the battery.
Higher-capacity batteries are bigger and heavier and may be tricky to retrofit to a normal bike.
Batteries for e-bike conversions may be on a rear rack, on the bars or attached to the frame.
An easily-removable battery is convenient for charging and bike storage.

Most conversion kits come with some kind of handlebar-mounted display and control unit.
This may give you comprehensive information on a screen like speed, remaining charge and current settings, or may be as simple as a coloured status light.
Because e-bikes can only be pedal-assisted by law, there will need to be a sensor to detect that you're pedalling.
This will either be mounted to the frame and crank arm for hub motors, or may be integrated into the unit if it's a mid-drive motor.

Key takeaways

Think about where the battery is going to go on your donor bike.
Depending on the design of your bike, there may be limits on the battery capacity that you can fit.
A conversion kit will come with some kind of pedal sensor so the motor only activates while you're pedalling.