If I worked for someone and paid them 1/2 of my earnings and did not receive a w-2 or 1099 how should I report income on my taxes? All checks were made payable to me and I cashed and gave her one half any cash was split 50/50.

You need to report the income on Schedule C, and then deduct all legal deductions.

Either report the full income and list the half you gave to the groomer as sub-contract costs, or only list the half you kept; either way is acceptable.

If you have income over $400 after the expenses are deducted, then you also need to complete SE for the self-employment tax.