Here are a few ways:
1. The tax liens expire -- If you can run out the clock, taxes generally will expire 10 years after they are assessed. There are a number of ways -- that the clock can extend past 10 years -- a. you file bankruptcy during the 10 years b. you file an Offer in Compromise (and it is rejected). c. the IRS has you sign a waiver extending the statute of limitations (not very common anymore).
2. An Offer in Compromise is reached and the debt is settled. (Everything you might want to know about Offers or settlements can be found here Offer - Rule Changes.)
It's worth noting that a tax lien is usually filed: a. when the Offer in Compromise process begins - and removed later b. you are placed into currently-not-collectible.
3. The tax debt is brought below $25,000.00. If you can pay your debt down under $25,000 - the IRS will remove the lien if you get in a payment plan on the rest.
4. The tax debt is paid in full. Why of course :)
5. You get the debt below $50,000 and enter an installment agreement. This streamline agreement is for people who have NOT had a tax lien filed against them YET...(If you already have a lien against you -- you won't have it removed).