Make the photos you bought the lens for. For each feature of the lens that is important for you, make a photo that utilizes it. Only you know why it is important to you, so you can construct the best test photo. For example, I really hate having color aberration around tree branches in front of clear sky, so I'd test for that.
Make sure the lens has an opportunity to show its best. Give your camera a secure support (sturdy tripod on level ground, legs as short as reasonable, central column not extended). Use a lens hood, avoid protection filters. Unless your scene has a lot of action, use mirror lock-up, remote control or self timer to trigger the shutter. Prefer contrast-detect focusing or make sure the phase detection sensors have correct micro-adjustment.
Analyze the photos and see if you are satisfied with them. If not, analyze if the bad aspects can be attributed to the lens, some other piece of equipment or your technique. Ask here if you're not sure.
Making the photos, you will notice any obvious deficiencies. No lens is perfect, no matter how much it costs. Engineered products are always results of a series of compromises. If the results look good, stop worrying and make more photos.