how to turn on gameboy?

The power switch is here on the top

(:

You'll need batteries.

If it's an original Gameboy or Gameboy Color, make sure the batteries you are using are still good (use a battery tester or just go grab a fresh set and see if it turns on with them.) Give the cartridge space a good blow into to make sure it's not dust or dirt thats stopping the game from running, and do the same for the cartridge itself. If it still doesn't turn on after a few flicks of the on/off switch, it may be faulty.

If it's a Gameboy Advance or any model after, make sure it has been charged. The system should be able to turn on even if the game doesn't register due to dust. Again, if it still doesn't turn on after a few flicks of the on/off switch, it may be faulty.

If you believe it is faulty, you can try to fix it yourself if you can, or ask someone experienced to, or just buy another one (they aren't all that expensive.)

ASSUMING you have a fresh set of batteries (or full charge of the rechargeable battery) & the system is still in good working conditition, there's generally a PHYSICAL SWITCH next to the cartridge slot. On the ORIGINAL Game Boy (the big grey brick that utilized 4 AA's), the switch would be on left of the top of the system (with the screen facing you). Once you turn on the Game Boy, it will lock the cartridge in the system so it cannot be removed until you turn it off (which is useful for some "friends" who want to disrupt your game may yanking the game cart out). This feature was NOT extended to future revisions (like the Game Boy Pocket) & upgrades (like Game Boy Color & Game Boy Advance series).

batteries?

Depends which version of the Gameboy you have, the original has an on switch on the top next to the cartridge slot, and you need to make sure it has fresh batteries inside.

You buy a charger for the Gameboy or maybe the Gameboy you got is broken