Hi!
It varies greatly from state to state. If you can afford it, consult with an attorney to guide you in the right path.
I have had to settle two estates - both without wills. Generally your local clerk's office will help you out a great deal. Both Oklahoma and North Carolina had a simple process for getting appointed executor of the estate (in N Carolina it was officially called "administrator") - It has always been the next-of-kin that should be appointed to this position ie Spouse, children (oldest to youngest), and then I forget if it would go back to parents next or a sibling... but you said your mother has already been appointed so no worries there.
State taxes in Oklahoma were limited to the filing fees (280.00) and in N Carolina they were .05 percent (not 5%) plus filing fees of about 200.
Federal taxes (at the time of my dad's passing-two years ago Thanksgiving) unless there was at least $600,000 in assets there was no tax liability...
She should be required to run a notice to creditors in the local paper to find any possible outstanding debt. Contact the Legal ads department - they will know what is required.
If any debt is outstanding, then they have to be paid first.
After that things will have to be run according to the will, if there isn't one, then it should be up to the administrator/executor to do with as they please.
Chances are pretty good that if there was any substantial assets, there was a lawyer involved in setting up the will, and would be able to help in direction of everything.
When everything is done, you have to submit an account of everything that was done (essentially a paper trail of the assets).
If your mom has brothers or sisters, I hope that every one is very close and that the will was very precise, and most precious items were divided before her passing.
I personally have seen my extended family be divided three times now after the passing of someone close - it brings out emotions that are very hard to deal with. Support your mother in every way that you can. Even when a parent's passing is expected - it is very hard to deal with.
I wish you well through these tough times, and hope this helps.
Good Luck,
Vic