Hybrid = plant that grows from a seed that was formed by fertilizing the ovaries of a plant with pollen belonging to another variety, species or genus of plants.
The easiest way to obtain a hybrid seed is to remove the anthers of a flower before they fully develop, otherwise they might scatter their pollen on the ovaries. After removing the anthers, cover the flower with a paper bag and wait for the pollen of your other rose to come to maturity (in case the two roses don't bloom at the same time). Then use a brush to take pollen and gently touch the ovaries of the rose covered in paper bag and close it again after you finish.
Crossing a red rose with a white one won't guarantee a pink hybrid because most roses available commercially are also hybrids and depending on their ancentry the genes are expressed in different ways. Whatever the colour that results it will be a beautiful one, mainly because all roses are beautiful in their own way.
When you see a fruit is formed in the middle of the covered flower, you can remove the paper bag and allow the fruit to mature before collecting the seeds. Don't forget to label the seeds and the seedlings because it will take a few years until the new plants will bloom for the first time and you might forget what you have crossed.
The most interesting part is that your crossing might result in plants that will have flowers of different colours - I mean that every bush will have one colour, but different from other bushes grown from other seeds.
The two roses that are to be crossed don't have to be planted next to each other, but you can transplant them if you want to. Transplanting is easiest when the plants are dormant, but you can also transplant them when they are green provided you disturb their roots the least possible and water them very much before and after.
Update: For better understanding of the morphology of flowers I copy here a picture provided by Mariana Ruiz LadyofHats on Wikipedia.