There are two ways to find out the uptime of your host.

1) Many hosts now have an "Uptime Monitored By..." graphic on their web site from a 3rd party uptime monitor, which you can verify as proof of the host's uptime.
2) Open an account with the host and monitor your individual web site.

Don't take the graphic on the host's web site at face value. Be sure you click on it and see how long it has been used to calculate the uptime. Some hosts with frequent downtime simply reset their service each time they have an outage. IMO, 99% uptime going back a year is a much safer bet than 100% uptime going back a week.

So lets say you find a host that has had great uptime for a few years. Its pretty well guaranteed that this host is reliable, right? Not necessarily. Many hosts have their own site monitored, but when you sign up with them your site will probably be on a different server than the one being monitored. Some hosts even go so far as to put their web site on a different host, so that "their" uptime is really another company's uptime.

While not entirely reliable, the uptime graphic on a host's web site is a great starting place for determining the host's uptime. Unfortunately, you can't be 100% sure until you've actually signed up. This is where the second method comes in to play.

1) Do not ever commit to an annual contract if you have never used a service before. Only sign up with a monthly plan or a free trial, if available. This way, if the company proves unreliable for any reason, you are not stuck with them.

2) Sign up directly with a 3rd party monitoring service and have them monitor your web site (rather than the host's site).

3) Give it at least a couple months. The reason you want to wait a few months is because some hosts massively oversell. When you first sign up with these types of hosts everything is great. In time, however, their servers fill up and become overloaded and you begin to experience downtime. If you haven't committed to a contract, you can leave at this point.

If, after a few months, the uptime is still really good, you are satisfied with support, and you feel completely safe with your new host, then you can go ahead and give some consideration to an annual contract to get a discount. (IMHO, contracts are rarely a good idea, even with a discount. Its ok to pay in advance only if you are certain your host will give you a refund should you wish to leave partway through, but that is a different topic.)