When you enter the website you search for a fragrance or brand. In my case I was looking for Keiko Mecheri. When you find fragrances that you are interested in you just click the sample box. I recommend using Fragrantica and Basenotes as additional sources for information if you are looking at fragrances that you have not tried in a store. After you have your shopping completed you fill in all the info, pay and wait.
After a few days you get a nice envelope that contains this.
So this is basically how it can work. My impression of First of Fragrance is that everything went very fast and smoothly so I feel that I can recommend them to you. If you are interested in sample from only one specific brand I suggest however that you contact them or look at their website as there are often very nice sample kits.