How do I find out if my deceased mother had a Will or who is in charge of her estate if she did not?

First, do the easy things, though there is a good chance they won't work: ask anyone whom she might have trusted with a will, or at least dicussed one with (any siblings of hers; any other children of hers [i.e. if you have siblings]; old, trusted friends; her lawyer and accountant, if she had them and you know who they are) to see if they have a copy of or know anything about a will. If no one has come forward to volunteer information to you, probably no one does, but it costs nothing and takes little time to ask around.
Second, file an action in probate court in the county in which she lived to be named the "personal representative" or "administrator" (either term may be used) of your mother's "estate" (everything she left behind) based on the fact that to your knowledge, there is no will. When there is no will appointing an executor, the court will appoint someone, generally the next of kin, like an adult child, to be the personal representative and have legal authority over the estate, to collect the assets, manage any property, pay any final expenses or properly submitted debts which people had against your mother, and then finally distribute whatever is left over after expenses/debts to the heirs who inherit under "intestate succession" (the rules for who gets what when there is no will--if your mother did not leave a husband behind, that will be her biological and adopted children, like you, but not any stepchildren).
Once you appointed by the court as the personal representative, you will have the legal authority to access her home, to collect and protect her assets, and to remove her boyfriend from the home if he is not on the home's title/deed. You would need the help of the courts to do these things if he still won't cooperate, but you'll have the legal right to have the court's help you once you have that authority. You'll also be able to access her bank accounts, investment accounts (if any), her safe deposit box, etc.
Note that "boyfriend" is not a legally recognized relationship and does not entitle him to inherit from her. He can keep his own belongings in the home, of course, and may have an interest in anything that was jointly titled to or provably owned by the two of them, or which she owned "pay on death" or "transfer on death" to him, but he will have no right to anything else of hers.
Ideally, hire a probate lawyer to help you. If you'd rather not, or can't afford the assistance, you can do this yourself: contact the clerk's office at probate court, explain that you mother passed and you do not believe there is a will, and ask for instructions. 
Good luck, and please accept our sympathy for your loss.