In the early days of the Mega Drive, the biggest hindrance to playing import games was the shape of the cartridges themselves. A Japanese cartridge won’t physically fit into a UK machine, although a US (Genesis) cart will.
The easiest way to play these old Japanese games is with anything that you can put in between the machine and the cart to bypass the cart slot. Import Game adaptors can be a little tricky to find sometimes (Ebay is usually the best place to look) but you can use a Game Genie instead. A more drastic option to get these games to fit would be to file down the edge of your cartridge slot to give you enough room. – this is not something I’ve tried myself but should be relatively straightforward.
After a while, publishers cottoned on to this and put extra protection in their games to prevent them working with simple adaptors. This generally applies to the later releases in the Mega Drive’s life, although there is no precise list of which games are protected. If you are lucky, you might be able to get an Import Adaptor that bypasses this protection. For example, a US version of Sonic 3 will only work with some adaptors and not others. Strangely though, if you use a PAL Sonic and Knuckles Cartridge and lock on the Sonic 3 cart, it works!
It is also possible to modify your console to bypass the region locking altogether and there are website that offer this as a service or sell pre-modified consoles. This is the costlier option but at least guarantees you no compatibility issues