What's the best way to remove a boil?

See your doctor. A boil is serious skin infection that should not be treated by home remedies. Especially with the increased incidence of MRSA infections, you should see your doctor for a definitive diagnosis and treatment. Squeezinig or attempting to "pop" these infections frequently leads to spreading of the infection under the skin.
Boils, infected skin. Boils are "pus under pressure". The best way to treat this is by sterilly draining the boil. The doctor uses an antiseptic and drains the boil by lancing the skin with either a needle or sterile blade. Then squeezes out the pus. Sometimes a drain is needed. Other times it is just kept open every day by squeezing out more pus and keeping an antibiotic ointment on the surface of the skin.
Compresses, antibiot. Hot compresses can safely open a boil so it naturally drains. However this can depending on location can take several days. Oral antibiotics combined with oral bromelain, which increases tissue penetration will resolve it faster. If very painful and large than surgical drainage will give immediate relief but will leave a small permanant mark.