Here is the situation...

What we have...

1. My wife is on H1.
2. I am on H4.
3. She got a W2 wage summary.

a. What are the tax forms we need to submit.
b. We are living in the state of Georgia. So do we file the state tax returns along with the federal tax returns.
c. Also, we spent around $400 on her medical expenses as they were not covered under insurance, can we claim these under medical expenses.
d. I do not have an SSN or a ITIN. How do I proceed further.

Please clarify and thanks for any help.

You can file resident tax return as Married Filing Jointly. You will get standard deduction of $10,900 and exemptions. Read about H1-B tax filing: Your U.S. Tax Return: The U.S. Visas

You MAY have to wait to file; it depends on WHEN your wife started her H-1 visa.

You will have to apply for an ITIN by submitting Form W-7 with a notarized photocopy of your passport.

Your wife will then sign the federal return, then you sign the return and W-7, then staple the notarized photocopies of the passport to the W-7 and paper clip both forms to the tax return. You then mail the tax return to the IRS at the address in the W-7 instructions.

The IRS receives the W-7, issues the ITIN, inserts the ITIN on the tax return and processes the return. The IRS then mails the ITIN to you in a separate envelope. This process takes between 4 weeks and three months, depending on the workload at the ITIN processing center.

You then neatly print the ITIN on the GA state return and mail the return to Georgia.