site down investigation

I'm rather new to web site administration so i would greatly appreciate some help.

My site has been going down quite frequently and i cannot figure out why. I'm on a shared server at OLM.net and the site goes down once a day or once every 2-3 days which is quite unacceptable. We are still small and we dont get a lot of traffic. We want to have decent reliability before we start heavily marketing and getting more traffic, however i cant seem to figure out how to get to reliability.

I'm open to any suggestions at this point. If its my host, i'm willing to switch if you can suggest a better one. I also understand that it might be because of the shared server, but i want to know for sure that it is before going dedicated, is it my scripts' fault or the server?

Any advice with this would again be greatly appreciated.