Using a base prior to eyeshadow application is very crucial if you want your eyeshadow to stay on longer and show up more vibrant. Below are a few methods you can prep your eyelid for eyeshadow.
Concealer + Power
This is definitely the easiest and cheapest method. All you have to do is apply a thin layer of concealer over your eyelid and set with some loose powder. It will help soak up some of your natural oils and prevent your eyeshadow from creasing.
These only work with powder eyeshadows. Applying a cream eyeshadow as a base will allow your powder eyeshadow to have something to grab onto so it does not fade as easily. Remember to apply the cream eyeshadow sparingly though. If you apply too much, you risk ending up in crease city. I also do not recommend this for those with oily skin because your makeup may just slide right off.
Product Rec: MAC Cream Color Base ($16.50)
I have seen people from other blogs and sites use Vaseline as a base but I personally do not recommend it. Like cream eyeshadows, the petroleum in Vaseline can make your eyeshadow slide right off if you have oily skin or apply too much. This is best left for pros or for a dewy look.
These usually come in cream or liquid formulas that dry off to a powdery finish. Most of them will work with powder, cream or gloss eyeshadows. Some of them even come in colors that match your skin tone to help even out discoloration on the eyelid. Since they are specially formulated to help prevent creasing and fading, I would recommend using primers over all the above for both beginners and pros.
Product Recs: MAC Prep and Prime Eye ($16), Urban Decay Primer Potion ($15) and Lumene Eyeshadow Makeup Base ($10)