My father died and now am the owner of his home. However, my two brothers lived with him at the time of his death without a lease. They are both unemployed. The pay for the utilities they use but they don't pay rent. I just received the house so there is no lease.

Were you awarded the home in a will?

You give them written notice to vacate within the deadline allowed by your state, usually 30 days. Then you trot down to your local courthouse and file for eviction (2 of them) if they don't leave. If they still don't leave by the end of the eviction, you pay a sheriff or deputy to forcibly remove them. You cannot change the locks until that day.

You give them written notice (at least 30 days in most places) to get out. If they don't, you sue them in court.

You evict them the same way you would evict a tenant. Any question on law needs to include your general locale as laws vary by area..

First, can we assume that a deed has been issued by the executor of the estate in your name and recorded with the county? Until that happens you are not the property owner.

Second, have you tried to work with your brothers, asking them to pay a fair market rental? Or are you trying to sell the property? Or do you want to move in yourself?

To evict you need to give them written notice (generally 30 days but the length of the notice depends on locale) to vacate. If they do not vacate by the deadline, you must go to your local housing court to get an eviction order. A hearing will be scheduled at which an eviction order will be issued (assuming they can't convince a judge they should stay). If they still refuse to vacate, you will have to hire a sheriff to physically remove them,

You should, not legally but morally, go and talk to them.

Now that you own the house ( I will assume it has finished probate and the deed is now in your name)

You should inspect house, and have it inspected with a outside inspector.
Since they are now also liable for any future damage.
Meet with them, and set a price for the rent, if you wish to rent it.

If you do not wish to rent it, ask them to leave.

You will from the legal side, give them written notice to move. And if they do not move, file a formal eviction.