I said simple, so I’m gonna make bullet points for those who skim read only. For you who want more detailed info, it will be after this text.
1. Clean all your pruning tools.
2. Prune all the canes for height. You determine the height you want. More info below
3. Cut to the base of the plant all canes that are damaged, diseased, broken. Also any canes that are growing towards the center of the plant or that are crossing over another stem.
4. Cut to the base any stems that are smaller than a pencil.
5. Thin the rose plant buy cutting more canes so there is room for each remaining stem to move with the wind and to grow. Leave the center of the plant uncrowded.
6. When pruning the stems develop good pruning technique -- see below.
7. Rake up all the refuse under the plant and dispose by burning or putting it in the trash. Don't compost rose cuttings.
Here is one way to clean your pruning tools, I am sure there are many others.
In a small container mix a small amount of bleach and water - a 1 to 10 mix is recommended or about 2 Tablespoons of bleach and 1 1/4 cup of water. Wet a rag in the solution and wipe down all your tools. Or immerse your tool in the bleach water and then dry. Roses can harbor diseases and if you have more than one plant, you do not want to spread whatever may be ailing one rose to the other.
Prune for Height
In this part of the country, (the intermountain west) you can prune your hybrid tea roses to about knee high or 18 inches. But what I have decided over the years is to prune and take notes to remember the height you pruned and decide if the rose bloomed in the way you wanted it to. Generally, the fewer stems you leave after pruning means you will get fewer flowers, but they will be larger flowers than if you allowed most of the stems to remain on the plant. If you prune to about knee height your rose may bloom a week later than those who pruned their roses to a higher point.
I have a hybrid tea rose (Double Delight) that is right in front of my brick faced garage facing south. The brick and the southern exposure cause the rose to bud out sooner than any others. I prune that one the shortest of all my roses - 18 inches or so. It is a very old and vigouous rose ( about 25 years old) and has a large healthy root system so I know it will grow to about 40 inches tall during the season.
I have another hybrid tea (Mr. Lincoln) that grows in the back yard and each year as the trees around it grow, the plant gets more and more shade. This plant is about 7 years old and because of the shade, is not very fast growing. I prune it to about 36 inches, so when it does bloom I can actually see it out my dining room window.
So, you decide how you want your roses to bloom, take into consideration their health, where they are planted, their growth habit. If you keep notes on how you prune it one year and then what you thought of the results (flower size, flower number, plant height) you can decide if you want to do it differently the next year.
Cutting out canes
I like to cut all the canes to an approximate final height and then start to prune for shape and thinning, etc. First thing to cut out are all the DEAD and DISEASED canes. These should be pretty obvious, the dead will be woody, dry and brown and break if you try to bend them. The diseased canes will be black or purple with holes or soft spots on the stems.
Now, check for stems that CROSS OVER another stem. Cut them out. The crossing stems will rub and open up the cane and make it susceptible to pests and disease.
Cut out any BROKEN stems.
It may be that not all of these canes have to be cut to the ground, maybe you will just want to cut to an outward facing bud to encourage that cane to grow outward and away from the center.
Look for stems that are PUNY, smaller than a pencil and cut these out. The general idea is that you want to allow for air circulation in the plant, so by cutting out the smaller stems and the crossing stems and the stems that are growing towards the inside of the rose, you will open it to more air circulation and, thereby, have a healthier plant!
I like to add compost around the base of the plant and, then an organic fertilizer after pruning, then after the first and second blooms. Don't fertilize in late summer, early fall.
I hope I have made the idea of rose pruning easier for you. Pruning is not something to be overly concerned about, nature has a way of producing beautiful flowers while you learn the techniques. Roses are hardy plants and it would be difficult for you to kill the rose by pruning it incorrectly.
See my Pinterest page on rose pruning here https://www.pinterest.com/gardenbuzzidaho/simple-rose-pruning/