You need to know what kind of tenancy they are under BEFORE you even purchase! You need any leases from the current owner, a transfer of any security deposits and last months rent, list of exactly who is in the unit etc etc.
You say you want to occupy one of the units so just give them a 30 day notice. What about the other tenant? Do you want to keep them? Do you want to renovate the unit? You may just want to get rid of both tenants.
If you want to keep one of them, at a higher rate, you need to terminate the current tenancy and offer them a new one at the higher rate. However, you may not just want to increase the rent. You may also want them to fill out an application to be sure they can afford the higher rate, you may also want to offer them a written lease with your terms (like no pets, no smoking etc) or other terms and conditions.
So I guess what you might want to do is concentrate on the unit you want, get that vacant and in the meantime just keep going with the other unit. Once you get your unit, you can then turn your attention on the other unit.
Assume for the moment the are tenants at will. You need to send them notice a 30 day Notice. As an example if you served them this week, they would have until the end of February to get out. If they don't leave, you have to go to court.
Just my two cents.