What area are you looking to build in?

In slc where buying a house and i feel like theres enough space to build another one on the side i would want a basement with 3 rooms one bathroom and then the main level 2 or one bedroom and one bathroom and kitchen and living room and dining room

Flori... Where is SLC?

Glendale

Start with your local zoning office to see if a secondary residence is allowed, and what restrictions that you may encounter. If sallowed, then talk with a local architect. Good luck!

Contact local Architects or Design/Build firms and find one you like who you think you can work with. They'll guide you through the process and provide you with the advice and service you need to move forward.

Ah...CA. Start by using the search tool here on Houzz. Meet with a few, pick their brains and move forward with the one you have a comfort level with. You need to start with someone you feel comfortable with then you can do your do diligence and check their references and past work.

And if it that doesn't work i would like to make the home where buying bigger its a one level house and idk if there anyway to make a basement or make it bigger some how?

If you truly want to know what your lot will fit, search out a local civil engineer and have them do an evaluation of your property for all factors concerning a new home. Those should include (but not be limited to, as I don't know CA and your township ordinances): Building envelope, permitted lot coverage, impervious coverage, etc. Then once you know your maximum allowable footprint and square footage, you can take that information to an architect. Some architects are able to perform this assessment for you directly too.

Good luck with your project!