The easiest way to begin experimenting with rose hybridizing, especially for the beginner, is to simply let some of your roses self-pollinate themselves, so they will "go to seed" and set hips. I have found that Playboy, Hurdy Gurdy, Peggy T and Fairhope are some of the easiest roses to set hips, and there are many others. Let the rose hips stay on the rose bushes at least four months before harvesting.
Everybody has a story to tell of how their grandma would stick a piece of rose stem into the ground and then place a Mason Jar over the stem to make it grow. There are tales of how the early American settlers of the 1800's traveled to the far reaches of the wild west in covered wagons, with grandma bringing along "starts" of her favorite roses from back home. Perhaps the treasures of these "monsters on wooden wheels" were raided, and they discovered the Yellow Rose of Texas hiding under the bonnets of the women. Or maybe the settlers used their precious "starts" to barter for provisions along the endless dusty trails.
Learn when it's safe to transplant seedlings. The first two leaves visible are usually "cotyledons," or seed leaves. Once the seedling grows several "true leaves," with a more typical rose leaf appearance, it is more likely to survive transplanting. It is also easier on plants if they are transplanted to a larger pot for a year or two, and then transplanted outside.