As someone who converted to Orthodox many years ago and had to learn to fast as an adult, I can't agree with Kolokotronis strongly enough -- take it easy and go slow. The first step, which can take quite a while, is to learn how to do without meat. Doing without fish and dairy products is the hardest step, and I honestly wouldn't recommend jumping into that unless you decide that you are going to formally become a catechumen.
It took us years to get to the point where we were keeping the fast fully as a complete family, and even now I confess to eating fish more than is "officially" allowed. This is pretty common "corner-cutting" in the northern Slavic traditions, since non-backboned seafood (which the Greeks have in relative abundance) were not traditionally available as sources of supplemental protein in those countries.
Just enjoy the services, read good material, get to know local Orthodox Christians, and let nature take its course...
I have a question: at what point do kids go though catechism? If I convert, are my kids included? (Actually, my last one needs to be baptized--we have never had a church community we called home long enough to get him dunked.)