In the FaceBook app, tap on the lines icon at the top left so that you can see the side bar. In the side bar tap on your name at the very top. When you see your profile page, tap on your profile picture (or the place holder). You should get options to either view the picture or upload a photo.
Same for the cover photo. Tap on it for the option to upload a photo.
In both cases the photo you want to upload must already be in the Photos app.
You can also go to FaceBook in Safari, though it is a bit trickier.
Like before, you want to choose your profile by tapping your name at the top left of the left column. If you don't see the column go to the top of the page and tap the Facebook icon in the header. This takes you to the standard newsfeed, with the column at the left.
To change the profile picture tap the camera icon in the bottom left of the current picture. One of the option should be Upload Photo. Again, the photo must be in the Photos app for you to upload it.
The Cover Photo is a bit harder. If you tap on it anywhere but exactly the right spot it just take you to the cover photo album. I've occasionally tapped it just right, but more often not. In this case it's easier to upload the photo to FaceBook as normal, then, when viewing it, choose the Make Cover Photo option that appears below in most views. You can change your profile picture this way too.
It wasn't until recently that you were able to do either of these with any success. The FaceBook app didn't have the feature and the website wasn't tap friendly. That's not Apple's fault, it's FaceBooks fault for weak mobile apps and mobile un-friendly web sites. That has been changing, rapidly, as FaceBook has realized that their future is mobile, as are the futures of most social networks.
Good luck.
