I am going to cut out the wall in my garage under my stairs to build a small room. When I put up the door I have to use a header because it's a load bearing wall. Do I need to make the header out of 2x10, or something else?
For door openings up to 36" (nominal) and for structures with no more than two floors above, it's a safe bet that doubled 2x10s are adequate as a load-bearing header.
Without more detailed information, that's as much as I can say.
There are alot of factors in sizing beams. Without more information we go to simple spans, simple load cases.
If the door opening is 3'-2" R.O., and it carries a 24' roof span with 25 PSF design snow load AND 24' floor load with 10PSF dead load, 40PSF live load, (2) 2x6 DF #2 more than carries the load. If it is only roof load, then it can support more roof span (over 50'). Just make sure no concentrated loads from beams or girder trusses land over the door opening; if they do I would recommend consulting a professional.
Point is, (2) 2x6 should be well enough if you can ensure absolutely no concentrated loads are on the beam.