To cross one plant with another, you need to do 2 things.
1. put pollen from the father on the stigma of the mother.
2. keep stray pollen off the stigma of the mother.
OR, plant the 2 side by side and hope for the best.
Assuming you want to be surer of the parents, then those 2 steps are important.
Peppers aren't hard.
Open a flower bud that is about to open. In the center is a thin thing pointing up. The end of it is the stigma, the female part. Around it will be the anthers, the male parts. 5, generally on a pepper, I think. They look like bags or bumps surounding the stigma. They are only connected to the flower at the bottom of each anther.
So remove the anthers. Do this on peppers just before the flower would have openned naturally. Do this by pulling out on each anther, because you don't want to hurt the stigma.
Then from the plant you want to be the father, you find a flower that has been open for an hour or more. Try to get some pollen out of an anther. It should be a dry powder. If not, then either you are too early, and the powder isn';t dry yet. Or you are too late and the pollen is gone. generally, with peppers, you have plenty of time, the timing isn't so critical, I mean.
So using a toothpick, fingernail, or artist's paintbrush, gently put some pollen on the end of the stigma.
Now wait until the resulting fruit is ripe, and then dry the seeds if you aren't going to plant right then.
An alternative to removing the anthers is to use a male-sterile pepper. They can be obtained from the Germplasm Resources Information Network (GRIN). They are quite willing to send them to you if you plan to breed peppers, but navigating through the GRIN website is a pain at first.

The principle is the same with other plants, but some have odd shaped flowers that are hard to emasculate (remove anthers). Some even have stigmas and anthers that are hard to recognise.
Some plants are even easier than peppers, some like an Ethiopian grin called Teff, have never been successfully been emasculated. The plant them side by side and hope is the only way found to cross Teff.
Peppers aren't a bad choice for starting hybridising.
A potential problem. There are several species of wild pepper,and several of those have been domesticated. Not all of them will cross.
But nmost domestic peppers in cultivation in the North America and Europe and Asia will cross. The South American ones are more varied, but still most will cross, just more exceptions.
You shold know that pollen is killed on contact with water or alcohol. Pepper pollen is long-lived, and if you use a paintbrush to pollinate a pepper, then later use it to make a diffeerent pepper cross, some of the origional pollen from the first cross may still be alive on the paintbrush. So sterilise the paintbrush each time you change pollen parents.
Pepper pollen can be stored dry and cool for a long time. Years if dried well and frozen. Other plants can have pollen that only lasts a few minutes, like rye pollen on a hot day.
Walter