How do I make a bed look upholstered on sides and end?

The box springs or the mattress?

I will assume you mean the sides, head, and foot of the bed. You can buy some plywood or paneling, cut it to whatever dimensions you want for each. Then you could glue batting or foam of some kind to the board. Cover the batting/foam covered plywood/paneling with fabric of your choice. Staple the part that you fold over to the backside w/ a staple gun. You then can hammer studs of some kind evenly in a diamond/square pattern across it and it will look tufted. There will be a lot of trial and error since you've never done this before. You may want to make a dry run by using cardboard for the wood to figure out what your patterns will actually be, use old sheets or some other material to figure out how much you will need to buy (allowing more for the extra you'll be needing for when the batting will be there). Work out all of that before you buy anything for the final product. Enjoy!

I just googled the word 'tufted' and on the page w/ the different sites, there's a lovely picture of a lady working on a tufted headboard (I think) so you could get an idea if that is what you would want. Also youtube probably has videos of someone doing it.

Here's a video tutorial: https://www.youtube.com/watch?v=NpJXanky3X8

Check out the explore projects button on the upper right of the window. I know there have been a few projects where people have made the upholstered side and end pieces that look upholstered. The end results have been really nice and seem easy enough to DIY.