I want to help an old friend that is down on their luck by letting they stay with me for a while. Is there a time frame where they can claim the right to stay? If they do not get their act together, I want them to leave and do not want to leave, what is the course of action?

Old friend or not, have a written agreement.
Whether they pay rent or not, they become a tenant after a period, usually 30 days and proof of receiving mail at your address. Some states have 'lodger' laws that allow you to get someone sharing your living space with you out sooner, but you still need protection, and there are separate laws regarding disposal of possessions.
I would give this person no more than 21 days. If the plan is longer, start rent after 30 days, escalating in amount each month. Have house rules too.

Old friend or not, have a written agreement.
Whether they pay rent or not, they become a tenant after a period of time, usually 30 days and proof of receiving mail at your address. Some states have 'lodger' laws that allow you to get someone sharing your living space with you out sooner, but you still need protection, and there are separate laws regarding disposal of possessions.
I would give this person no more than 21 days. If the plan is longer, start rent after 30 days, escalating in amount each month. Have house rules too.

The "30 days and proof of receiving mail at your address" rule is something that has been passed around on this forum, but I am not persuaded that it's valid. It will depend upon the laws of whatever state or country it is in which OP located.

But this OP has a distinct advantage here, by asking before helping out the friend instead of afterwards. Check out the "lodger" laws in whichever jurisdiction it is, and plan accordingly.

I agree spell it out in writing. My experience is that the law will rarely allow you to just throw or lock someone out of where they are living. So if they refuse to leave, you will likely have to evict them.