The most common cause of a ligament injury to the thumb metacarpophalangeal (MP) joint is a skiing injury--thus the name (skiier's thumb. Historically Gamekeeper's were reported to experience attrition of the ulnar collateral ligament from using the hand and thumb during specific job activities---thus the name "gamekeeper's thumb". In 2005 my own wife had her hand in the pole strap--a definite no no--- and sustained the injury to the "ulnar collateral" ligament. The good news is that if it is only a partial tear, effective treatment can be provided with a cast for 6-8 weeks. The bad news is that complete tears require surgery to reattach the ligament.
The thumb MP radial collateral ligament can be torn as well--and both ligaments can avulse with a small piece of bone as well. Xray will show this. If there is a piece of bone, fixation may utilize a smal pin or screw.
Postoperatively, a splint or cast will be necessary for 6 weeks or so, and full recovery may take 3-6 months.