The process of cross-pollinating occurs all the time in nature. Pollen is exchanged from one flower to another via butterflies, bees, and wind. In addition, botanists work closely with cross-pollination as a means of altering plants.
You can try to find out what happens when you cross-pollinate-or remove pollen from one type of flower and put it onto another type. It's not difficult to do this, but you'll need to have a basic understanding about the male and female parts of a flower, and on which part of a flower the pollen must be placed in order to result in fertilization, and ultimately, a seed.
Flowers contain both male and female parts, and often pollinate themselves as pollen moves within the flower from the male part to the female part. You can, however, move pollen from one type of flower onto another, essentially creating a new type of plant.
If you're interested in botany and this project, begin by researching the anatomy of flowers, and the processes of pollination and cross-pollination. You can use any flowers you want, but be sure to leave plenty of time, as you may have to repeat the experiment.
Once you put pollen from one flower on another, you'll have to hope that fertilization occurs. If not, you'll need to try again.