I know several Roman Catholics who have converted to Orthodoxy. They were made catechumens like everyone else, though their instruction (and sometimes the length of time) was tailored to where they were in their spiritual life.
The initiation rite may vary by jurisdiction (i.e., national branch of the Orthodox Church—Greek, Russian, Serbian, etc.). I think in general you would be chrismated (confirmed), but not necessarily baptized again. I seem to recall that a few jurisdictions receive Roman Catholics by confession (i.e., renouncing the Roman Church) and that's all. Not completely sure on that one though. It is best to discuss this with the parish priest if you decide to move forward with converting.
You certainly may visit a service, and you may participate in every way except for receiving sacraments.