I rented my place to a friend. She asked me could she move in three days before the day we had scheduled to move in. She was to pay me first, last and a deposit. However she only paid the deposit and part of the first months rent and refused to sign the lease agreement. I was told by a lawyer now that she did not sigh the lease it is now a month to month lease. She moved in on the 14th of last month. First I want to know is now long do I have to wait to evict her and what rights does she have not to have to move. Second what does a month to month lease mean?The bad part is also she was suppose to get the power turned on in her name, but since she moved in before I could turn the power on it is in my name and I am paying the light bill as well. I feel like I should just pay all her bills... lol.

Laws vary by state.
Generally, for non payment of rent, you give a 3 day Notice To Quit in writing, consisting of what is owed, what was paid, and a sentence just saying to vacate the premises. This is followed by eviction through your local court, which doesn't need a lawyer.
You can call your utilities and have service terminated or temporarily suspended. The latter would be best, but it will cost a small charge to keep it on hold.
You might want to tell her the process and that you plan to follow through, and then do everything after that phone call in writing. Also tell her that as a tenant at will, you can terminate her tenancy any time with just 30 days notice (in most states), and that a lease is to her benefit.
Of course you may not want her there anymore.

So she moved in, you arrange to turn off the power, set a date and tell her, she will have till that date to arrange it in her name.

You did not agree to pay power.

But if she is not paying the bills, you have to fillow eviction proceedings. A verbal "lease" is just a verbal month to month rental. Lesson learned, they never ( NEVER) get the key until all paper work is signed and all money is paid.

A month to month (or periodic) lease means that there is no fixed term for the lease. The lease can be ended by either party with proper legal notice.

As for shutting off the power, I would be very hesitant to do so. Generally, shutting off utilities or changing locks could be considered an illegal eviction. If you have something in writing that states she was supposed to have the electricity transferred to her name, you may get away with it. But I would be more inclined to leave it on and sue for the costs as part of the eviction.

Since she moved in on the 14th, If she does not pay the amount owed IN FULL by Sunday, then on Monday you give her a pay or quit notice. Since you didn't tell us where this is (Any question on law needs a general local as laws vary by area), we can't tell you how much time you have to give her. If she doesn't pay in full by the deadline, file for an eviction order.