Where and how does one have a will processed after the person whose will it is dies?

My mother died recently and my sister and I need to have her estate distributed. My mother had a will originally drawn up and "executed" (I hope I'm using that term correctly) in the state of Maryland. She spent the last several years of her life and died in Missouri, however. My sister lives in Missouri and I live in California. We are the only two heirs and my father died in 1993.

What do we need to do first? Where do we submit the will for processing - Missouri or Maryland?

It doesn't matter where the Will was made. What matters is where your mother lived. You probate it in her state of residency. If she owned real property in another state, you'll have to do an ancilliary probate. If she owned personal property in another state, that state will honor the probate from Missouri. Are you sure you even need a probate? You are her only heirs. In my state you could do this by affidavit. Did she own property that have documents of title like real property, stocks, bank accounts in another state? See-there are a lot of unanswered questions here. It would probably cost you about $150-200 to visit an attorney and get these questions resolved. You may not even need a lawyer for a probate. My state has "do it yourself" probate forms on line.

you file the will in either the county where she had real property, and then re-file it in the other state; or if she had no real property, file it in the county where she was living when she died.

Submit the will to probate court in the last state she was a legal resident of. Having the will "executed" means that it was made formal, and a valid legal document.

You need to go to the lawyers that made the will with your mother. They will help you go over the will and disburse whatever your mother wanted to go and to whom.