Every few years theres a new beauty phenomenon. You'll start reading about a coveted luxury version in magazines, see it mentioned multiple times on a popular blog, and finally a inexpensive option is on your drugstore shelves. Usually these trends are just a newly packaged version of a product that already exists (as in your BB cream is really just a glorified tinted moisturizer) and facial oils are no different. Most facial oil ingredients have been around for decades in your favorite serums and moisturizers, but now they are available as a stand alone oil based product.
Oils can pass through the lipid layer of skin, so they can be better at preventing moisture loss then a cream. While many oils are packed with antioxidants to create a protective layer over the skin, some do contain fragrant oils (citrus, jasmine, lavender, etc) which you want to avoid on the face because they can have potential to irritate skin and be phototoxic to skin when exposed to sunlight (as in cause discoloration).
THE BOTTOM LINE
These are not a must have skin care staple. Try a well-formulated moisturizer first. Skin is complex, and needs a combination of complex ingredients to be its best, especially when treating sensitive skin, acne, wrinkles, and sun damage. Relying on a single oil or even single product won't do your face any favors, so keep your expectations realistic. If you have stubborn, dry, flaky patches and your moisturizer isn't helping (especially during colder months), then perhaps consider adding a facial oil to your routine at night before your moisturizer. Oils are applied very sparingly, a few drops on your fingertips and press into the skin. Use them night only or on days where you aren't outside and exposed to sun since they can dilute how effective your SPF is. Theres really no right or wrong way to layer them with your moisturizer, but my first suggestion is to press them onto moist skin after washing. Jojoba, grape seed, avocado, almond and safflower are all excellent options and be sure to avoid fragrant oils.