How to file taxes when I have w-2 from two different states? Can I do both state and federal or do I have to go with someone to do them for me?(Colorado and New Mexico)

Which state do you live in?  CO, NM, or one state each?  Did you move?  Based on answer I can give a good answer for you.

We moved from co to nm. So my husband work about 8 months in co and 3 months here in nm.

You will file part-year returns for both states.  Your Colorado income will be taxed in Colorado, and your NM income will be taxed in New Mexico.  TurboTax will separate the income out to both states if the correct information is entered in your W-2s.  This FAQ provides the instructions you need to do this:  https://ttlc.intuit.com/replies/3302008