First, be aware that each rose seedling is a new, never-before-seen variety. If you plant seeds of 'Don Juan', you will get climbers, large bushes, small bushes, in a variety of colors, with a variety of scents, etc. What you can be completely sure of, though, is that you will not grow another plant of 'Don Juan'. That's true of any variety from which you collect the seed; they don't "come true" to the original type. The probability of your coming up with the next AARS winner is not very good. Kind of like winning at Lotto. However, among the many poor quality seedlings, you will likely produce some plants that you find interesting, and which may be well worth growing.
Most roses come from colder climates than Florida, and their seeds are programmed to survive a winter before they sprout. We can trick them into sprouting by giving them a "stratification" treatment -- a period of moist, cold storage. Rinse the seeds if they have a lot of fruit pulp on them, and wrap them in a moist paper towel. Place that packet into a zip-loc bag, and place it in the refrigerator (not the freezer). Be sure to include a label, indicating the parent variety and the date. Don't feed it to the dog or the spouse, as left-overs... After 4 or 5 weeks, start checking on the seeds every week or two. At some point, you'll notice little root tips poking out of some of the seeds. Carefully transfer these to pots of soil, cover them with about 1/4 inch of soil, water them in, and keep them at room temperature. They should emerge in a few days. Be careful in transferring them since they are quite fragile, and they tend to stick to the paper towel. It's very easy to break the root off of the seed. I use a blunt pair of tweezers for this process. Put the unsprouted seeds back in the refrigerator for another week or two, and check them again. Depending on the variety, seeds may continue to sprout for several months. So you'll likely make several transfers to warm soil, over that period.
Very young rose seedlings are quite susceptible to damping-off, a disease in which the stem rots at the soil surface. Avoid it by using a sterile planting soil to start with, not overwatering, and if you like, use a copper-based fungicide right after the plants come up. Another common problem with rose seedlings is that a high percentage of them will be highly susceptible to powdery mildew. It's probably best to discard those plants, since they'll not likely become resistant later in life. Keep the robust, healthy seedlings instead.