While there are common concepts and practices to pruning all roses, it does help to know what kind of rose you have before you start pruning. Whether it's a climber or a classic tea rose with the big buds we're all familiar with, or something more carefree like these knock-out roses. You want to have a good idea of what you hope to accomplish before you start hacking away at it.
The classic tea roses and roses in general, but mostly tea roses are susceptible to black spot and that's one of the main reasons that people prune them is to keep a good open structure that allows air circulation so that black spot's not allowed to form.
So what you want to be looking for in a tea rose is only three or four canes that open up in a vase shape, so that you have an open air space to the middle that allows air circulation. What you don't want are any cross canes or foliage laying up against each other, which will hold moisture and then promote the formation of black spot.
So you'll just want to go in there. Any of those canes that are in the center of the rose bush, go in there and prune those out down at the base so that you have that open air space or vase shape in the middle.
Now another reason that you'll want to be pruning your roses is to deadhead them, if you want to keep them to bloom. And everybody wants their roses to bloom as much as possible. Now the reason for deadheading is that when a flower or plant or a plant forms a flower bud, it acts as a signal to the rest of the plant. It sends a hormone or a signal back to the plant that says, "We're done reproducing and we don't need to make any more flowers." So if you want your plants to keep flowering, you need to cut off those seed pods that are formed to keep the signal from going back to your plant that says it's done reproducing.
So in any case when you're deadheading something, just find a rose hip or a flower bud and just go in and snip that off. It's as easy as that, and just discard it. It'll rot.
If you want to do a little size control, or you want to get rid of some branches that are crossing or in the middle that's inhibiting air circulation, you'll just go in, reach in, go down to where the next branch is that you want to keep, and just snip it off like that. And then whatever's left, again, you can throw it in the compost pile or discard it as you will.
One of the keys to pruning roses is you really want to make sure you have a good sharp pruners. Some of these canes can be quite large and in those cases you may want to use a Japanese folding saw. These are very sharp. They're very effective so be careful, but you can just go in and prune out the larger canes.
Concerning your pruner as well, you'll want to have what's called a bypass pruner, which acts like a scissors, and the blade moves past the other blade. You don't want to use what's called an anvil pruner, where the blade comes down and strikes a piece and does not pass by it like a scissors.
So those are the basics for pruning the various kind of roses. If you want to get more information, of course you can search on the internet, and there's loads of information on pruning specific kinds of rose bushes.