To do it properly you’d want a subpanel with an outlet coming off that. That is a smaller panel that takes in 220 and has the appropriate breakers on it for 220/120 circuits… appropriate based on the breaker size of the original line.
In essence you’re taking one ‘hot’ of the two that go into the 220 outlet and one neutral. It’s not particularly simple so if you’re not knowledgeable with this stuff I would recommend getting a pro…
What kind of light are you planning on running from the 120 outlet? Many old school core and coil HPS/MH ballasts can be rewired to run off either.