If my mother died intestate, what happens when her estate goes into probate?

This is a very broad question.  The first step is to determine whether probate is necessary at all.  Did your mother leave assets that were titled in her name?  If so, title must be transferred and probate is the method.

If your mother named a beneficiary on an asset (including a pay on death bank account), that asset will be paid directly to the beneficiary without the need for probate.

If your mother died with a few assets titled in her name, her estate may be relieved from probate administration under Ohio law.  The specific provisions of this depend on the value of her assets and her survivors.  If your mother had less than $35,000 in assets, or less than $100,000 in assets and a surviving spouse, the estate may be relieved from administration.  The local probate court can probably help you find out if her estate is eligible.

If your mother died with significant assets titled in her name, then you will have to open a probate estate.  I would not recommend attempting this on your own.  You should hire a lawyer.

In general, the steps for probate are:  petition to open probate & appoint a personal representative/administrator (folks can fight about this if they want to pay the cost of doing it), the administrator gathers & accounts for the deceased person's assets, the administrator researches & pays the deceased person's debts out of the decedent's assets, the administrator divides & distributes the remaining assets according to Ohio law, the administrator closes the estate.   The administrator and the lawyer are entitled to be paid from estate assets.

I trust this answers your question.