Welcome to Basenotes!
Simple glass vials are the norm. Sprays would be too expensive to use. However, sometimes you get sprays if the sample is directly from the manufacturer/designer.
You could use the applicator if you're really unsure about liking the scent after sniffing it from the vial but this won't give you enough juice on your skin to form a good opinion. Just use your fingertip to receive from the vial and to apply on your skin. You can also tip the vial directly on your skin. How much you apply is up to you but enough to spread to about the size of a quarter, etc. should be fine for starters.
For a sample, the best place seems to be the back of the hand or the wrist (either/both sides) because this will allow you to continue to smell and study the scent (the progression of the notes, longevity, and to some extent the sillage/projection).
Once you get a good sense of what it's all about, you could try some on your neck (sides, back, etc.), chest, or inside of your elbow to allow the scent to do all it can with your skin and for all of its possible effects.
Typically, a 1.5 ml vial allows for 2-3 tests on your skin--but this can vary.
If you're experienced enough to know what you like in fragrances, you should be able to tell whether you like the scent to purchase or not with these tests (in the case of most scents). Sometimes it takes more than just a vial and some people go for multiple or larger decants but in reality, experienced people can tell even with a few drops.