I live a few blocks from the lake so I have ridden it several times. I always use my own bike but I know there are plenty of places to rent from, I think Navy Pier offers that. That's a good place to start as well since you can go North or South, or both!
You can rent bikes in Millenium park. I would recommend bringing your own.
My suggestion is to ride the trail during the weekday to avoid any weekend rush. It gets very crowded, and is particularly dangerous. Watch out for those a$$holes who are training for the triathalon, zipping through crowds at 25mph.
I recommend starting around North Avenue, and riding south to 55th ave. Yes, that's the south side, but there isn't any creppiness on the trail. That, and there's fewer people, better views of the skyline, and it takes you right by all the museums, Soldier Field, etc. Going north is relatively boring.
and if you ride south, promontory point by the university of chicago has a really nice view of downtown for photos. just be careful after dark, i have known a few people who have been robbed on the bike path near 31st street and 39th street.
And don't be TOO afraid of riding in the winter (or at least some cooler weather). There's a lot of ice between Fullerton and Navy Pier, but it tends to be in pretty good shape south of there. No crowds. Beautiful views. Just keep your fingers and toes warm!
And if you come in the warmer months, I encourage you to take to some of the streets. Get a copy of the Chicago Bike Map (or look it up online). It'll give you an idea of what streets have the nice, wide bike lanes. This is a GREAT city for cycling and being bicycle-bound frees you of a lot of the hassle of parking, CTA routes, etc. You can really get out into the neighborhoods and see a lot of stuff that the average, weekend tourist would miss out on.
The lakefront trail is terrific. So much to see. You can rent bikes at several locations on the path. It's already been said, be careful. The path is very congested in some areas and collisions with pedestrians and other bikers do occur often. I'd recommend a bell, horn, or audible "Passing on your left" when attempting to pass someone. Additionally, alway stay on the right hand side of the lane, so it's easier for people to pass you. Enjoy your trip.
I've ridden my Snakeboard from Fullerton down to Navy Pier and back a bunch of times. Usually stop at the boat restaurant there at North Avenue Beach. If only there was a little Jeep trail. Wink Wink =o)
The wind (the Hawk) can be very strong along the Lake.
If you are planning a long ride, anything over 5 miles, you should check the weather report. A wind speed much over 8 miles an hour can stop you in your tracks. This can be really tough on Winter rides.
It would seem to make sense that the wind will be at your back for 1/2 of your ride but it may not work out that way. Due to the irregular shape of the lakefront it can seem that no matter which way you turn you are always riding into the wind.
It is fun to ride anytime but try to plan a short bike trip on windy days.