https://www.youtube.com/watch?v=kT6GI1u2DjgProper hand care is not talked about too often but it is extremely important for weightlifting. You need your hands to be in top condition all the time! If you can't grab the bar because of torn hands and/or calluses you will not have very productive training.
After training make sure you wash your hands to remove any excess chalk. Chalk will cause the hands to dry out and lead to additional tearing.
File Down Calluses
If the calluses on your hands grow to large they can tear or rip easily. The goal is to have calluses which are flat. To accomplish this I recommend a filing them down 2-3 time per week with a cheese grater type file. Always file your calluses after a long shower or bath then your calluses will file off very easily.
After filing down your calluses always use a moisturizer, salve, or lotion such as Burt's Bees Hand Salve, Badger Healing Balm, or O'Keeffe's Working Hands. When considering a moisturizer look for products that are thick, not thin and runny like a typical white moisturizer.
And always moisturize your hands throughout the day, especially after working out! Dry hands and calluses rip much easier.