Here's a link that gives basically all the info you could ever want on flower mechanics in the game. You'll probably want to click on the Simple Guide at the top and take a look at the Garden Layouts guide.
If you're only breeding with two flowers, you can just set them side by side as a pair. Keep in mind that this is not very efficient and will probably take you an extremely long time to get results unless you rely on visitor watering. You generally want to have multiple flowers breeding for the same hybrid at once.
Regarding the Mums, you'll want to read some of those guides on flower genetics to understand what's going on there. In a nutshell, though, you're breeding for genotype and not phenotype. Guides that just say to breed Purple Mums for Green Mums are wrong because they're focusing on flower color and not the genes. You'll have to breed for Hybrid Yellows first. Hybrid Yellows have a chance of give you Greens, but if you get Purple Mums
specifically from those Hybrid Yellows, then breeding those Purples together gives you a better chance of getting Greens. If you get "standard" Purples from White Mums, those won't ever make Green Mums.