A lot of your weight rests on the bike seat so soreness is common here, especially if you're a new cyclist and not "broken in" to riding. Usually, after a few rides, your body will get used to the seat and any soreness will go away.
If not, the seat could be adjusted incorrectly. Its top should be level with the ground or angled up or down very slightly for comfort (no more than three degrees). Check this by placing your bike on a level surface and resting a yardstick on top of the seat. Compare the ruler's edge to a distant rooftop or the horizon. If the seat's off, level it.
Equally important, the seat should be set so that when your feet are at the bottom of the pedal stroke, your knees are slightly bent. If your knees are locked or nearly straight, the seat is too high. This prevents you from supporting enough body weight with your feet and places too much on the seat, causing discomfort. So, lower the seat right away.
If you plan to ride a lot, consider wearing cycling shorts. These are padded and seam-free in the crotch area so that you're not sitting on anything that can chafe or pinch. They're also cut for comfort and are made of fabrics that wick moisture away from the body to keep you dry and comfortable. These days, there are many types of shorts, too, including baggies, which no one would suspect are cycling shorts.
Still sore? Another possibility is that your seat doesn't fit your body correctly. If that's the case, no amount of adjusting will ease the discomfort. The cure is finding a more appropriate seat. There have been impressive advances in seat technology in the last few years and you'll find many new models at bike shops that eliminate pressure on sensitive body parts. These sweet seats employ shapes, shock absorption and padding to prevent pain and increase comfort. The best place to shop for seats is at bike shops where you can try them to see how they feel.
Besides seat problems, bicyclists often suffer upper-body discomfort from gripping and leaning over the handlebars. Soreness in the hands is fairly common.
You can usually eliminate discomfort by moving your hands around regularly and relaxing your grip. Most regular riders wear cycling gloves, which help a lot, too. These have padded palms to cushion your grip.
If you experience lower back, neck, arm or shoulder pain while riding, it's probably related to your handlebar position. If the bars are too low, it forces you to lean over too far and rest too much weight on your arms. The bars might also be too far away or too close to you, which can cause discomfort, too.
Because it can be tricky to move handlebars (sometimes replacement parts are needed), we recommend having a bike shop check and make this adjustment. In most cases, the mechanic can move the bars and eliminate discomfort for nominal cost and you'll finally be able to experience biking bliss.