1) You have a right to stay in another member state (host) for three months without any restrictions.
2) After three months, if you are not (self-)employed, restrictions can be placed on you. In particular, hosts will require you to prove sufficient resources to support yourself, including health insurance. If you are not employed and cannot prove sufficient means, you can be removed.
3) If you lose your job, you have a right to remain as a job seeker for six months. If you do not find a job within six months, you have to prove to the host that you are actively seeking a job, and that you have a realistic chance to get one. If you cannot prove that, you can be removed.
4) You get a right to permanent residence in the host after legally staying there for five years.
5) It is currently unclear if you have a right to the six months of job seeking before you've had an employment contract in the host state.
While I'm not a lawyer, I have used these rights myself three times now so I've read through them carefully as well as the local regulations in the countries I worked in.
[0]http://www.europarl.europa.eu/factsheets/en/sheet/41/free-mo...