They consist of a laser diode (often wrongfully convicted of failure) and its driver, coil-actuated optics, and a photodiode array chip.
Increasing the laser power may make CD drives work again by making the light shine through dirt and contaminants on optics, but it's actually a side effect of an inadequate adjustment that will kill the laser diode faster. A real solution is to clean all optical elements in the beam path, which involves taking the pickup apart.
Adjusting the pots located on the CD module PCB can also help, even if those settings shouldn't drift over time.
Some might find more convenient to replace the whole pickup. They can still be found on eBay for around $30. Beware of sellers who re-package and advertise the pickups as exclusive, original replacement parts for consoles with ridiculous prices.
NeoGeo CD Front loader
Original reference: KSS240 (A)
Compatible models: The Sega Mega CD's one
NeoGeo CD Top loader
Original reference: H8147AF
Original reference: H8151AF