When you're bringing anyone new into your apartment, the first question you need to answer is whether or not you want to add them as a co-tenant. Adding someone to the lease while it's ongoing is generally pretty difficult because landlords don't like making lease modifications that expose them to additional risk. If you can convince them to add someone new to the lease, they will require the same application that you filled out in order to get the lease—usually a rental history report, credit check, and income verification.
Otherwise, they can live with you as an occupant—someone who occupies a rental unit without having signed a lease agreement with the landlord. A subletter is also considered an occupant, because their sublease is with you, rather than the landlord.
If your roommate is on the lease, then one benefit is that your landlord is more likely to take action quickly should they do anything wrong. Landlords sometimes don't want to get involved with people who aren't officially tenants. It also means that you’re both equally responsible for paying the rent in full each month and keeping the apartment in good shape.
As discussed above, it's harder (and sometimes impossible) to add a roommate to your existing lease agreement. And, even if your landlord agrees to it, they may bump up your rent because of the additional tenant. They may also increase your security deposit—if your state doesn’t cap how much they can charge, that is.
One more thing to consider: when you're the only one on the lease with your landlord, you have the ability to evict your roommate if they're not paying the rent or breaking the terms of their sublet agreement. If you're both on the lease, and there's a term that holds you "joint and severally liable," then you and your roommate have to be evicted as a unit—even if you're not doing anything wrong.
Each state has different rules for new co-tenants, but generally if you want to add someone to your lease agreement, you’ll have to get your landlord to agree. The best way to do this is to find someone who is as qualified as you and have them fill out a standard rental application or the building's custom rental agreement. Make sure that they meet the income and credit requirements first, and that they don't have a history of evictions. You can send your proposed co-tenant's application to your landlord along with a simple letter summarizing your request.
To protect tenants who need to live with family, most states have laws in place that give you the right to have someone move into your rental unit without adding them to the lease. For instance, New York’s so-called “Roommate Law” gives any tenant who is the only one on their lease the right to share their apartment with one other unrelated adult. (Tenants are always allowed to move family members into their apartment without adding them to their lease in New York, as long as the rental doesn’t end up being overcrowded according to local occupancy limits.)
Evicting a Roommate
Can My Roommate Sublet Without My Approval?