Not terribly difficult. Amtrak comes into 30th Street Station, which is on the western side of Center City. You ride 1-2 miles on city streets to the Ben Franklin Bridge, which crosses over to Camden (has walkways on the side). Camden is kinda dodgy, depending where you ride, but shortly you are out of it and can choose your route to Ocean City. It's actually very pretty riding through South Jersey and the Pine Barrens, etc. Probably about 70 miles all told. The local MS150 ride goes from Cherry Hill, NJ (just outside Philadelphia) to Ocean City yearly, so you can probably find some cue sheets online from their rides (like these: City to Shore Route Options & Rest Stops - National MS Society).

If you don't want to (or don't have time to) ride, NJ Transit has regular buses (think Greyhound type buses) from Philly to OC. The bus depot is in Center City, adjacent to the SEPTA Market East (aka Jefferson) Station. I believe with your AMTRAK ticket you can take a SEPTA Regional Rail train for free two stops from 30th Street to the Jefferson Station. As long as it's off-peak you should be able to bring your bike on board the train with you (although it might be challenging). NJ Transit also offers regular trains from 30th Street Station in Philadelphia (AMTRAK station) to Atlantic City, and then you could easily ride to OC (10 miles or so along the coast).