Since you mention nothing about a group's social contract, hopefully I cover all the possible ways to handle it . First, consult your group's social contract (if it exists) on the topic of torture, and if not now may be a good time to consider codifying some lines and veils for future reference.
Definitions: Any given topic can be considered as a line, a veil, or "fair-play"
Line: A line is something that a player objects to being in a game. Frequently I use the topic of rape as an example of a line. This is something that my group feels so strongly about, that if I were to have PC1 raped, the rest of the group would walk out before PC1 was finished packing up their character. Lines are things that do not get crossed.
If torture is a line to any of your players, you need to do a re-write of your torture/interrogation scene.
Veil: A veil is something that is difficult to experience "in-character", yet a player has no objection to it being used as a story mechanic. As other answers have mentioned, torture scenes can be huge and scenes of great transformation for a character. If you watch old movies (like from the 1940s or 1950s), love scenes / sexuality are commonly handled as a veil. The two characters start smooching a bit, the music crescendos and then the picture fades to black. Next scene, is "tomorrow morning" and either the two characters are in their bathrobes (if a married couple), or the movie has moved on (if not).
If torture is a veil, you should ask the tortured PC's player something like "This guy is going to torture your character. How long do you hold out before you start talking, and what do you say?" This gives the character the chance to figure out where they break, and also gives them the option to try to lie to the interrogator. If the player chooses to hum the 1812 Overture for the entire interrogation, you should ask them if they are sure they are sure about killing their character. This should be handled as something of a negotiation where both of you come out feeling good about the scene. If necessary, pull back the 4th wall's curtain a little bit.
Fair-play: This is somethign that your players all consider to be something they are comfortable participating in on a blow-by-blow level. Combat is a fair-play concept. NPC dialog is as well.
If Torture is a fair-play, you can go nuts. Give your torturer some personality and a bit of a style.
Ways to torture: I would encourage you to not do anything that is permanent. There are many ways to apply "pain motivation" without destroying a character's body. You can do cosmetic things like scarring (cut a flesh-wound, then rub salt/vinegar into it) or cutting off ears/nose/fingers. You can also attempt to bend joints in ways they are not intended to go. The arm-bar used in MMA tournaments is a great example. Straighten an arm and then try to bend the elbow backwards, it is very painful and the pain stops immediately when pressure is removed. If the character decides to not talk, you can push it the rest of the way, break the bone(s) and move on to another joint. Simply put, as debilitating as these things are your PCs can then heal that damage. Sure, maybe they get a sore elbow/knee whenever the weather changes, but that only adds seasoning to the character.
A final note on lines/veils: Once you have polled your players on how they feel about torture, your group's opinion is whatever the most conservative view is. So if even one player considers it a line, it is a line. If everyone thinks it's fair-play, I would recommend you give everyone a marker or other token. If anyone gets squeamish, they turn in the token, no harm, no foul and the rest of the scene is wrapped up as a veil topic.