How high you want to trim your trees is up to you. Often, people trim up the lower branches so that they a mow under them. You ever want to remove more than 1/4 of the live foliage in any one year. Removed any dead branches first. 

You don’t say what kind of birch they are. Birches should be pruned later in the year to avoid infection from bronze birch borers. Also, if pruned early in the year they will bleed sap like maples. 

Pruning can be to improve shape. Below are two articles that should help you. Stay away from using power tools like a chain saw. If your trees are too large, consider hiring a tree professional. 

https://www.fs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb5368392.pdf

https://extension.umn.edu/planting-and-growing-guides/pruning-trees-and-shrubs