'Bending' is a very common technique, particularly in the Blues idiom. It's used to raise the pitch of a note that already been struck to a higher pitch without moving your finger from the original note's fret position. It's achieved by pushing the string sideways, across the fretboard, thereby increasing the tension on the string. More tension = higher pitch. The result is the sound of a note 'bending' up to the next note in the melody line, riff, lick or solo. It's most commonly used for single notes, but can be applied to two strings at once.
1. Always try to use more than one finger to push the string. You may not always be able to, depending on the passage you're playing through, but using one finger is painful and more often than not you won't reach the desired pitch. If you use very light gauge strings, you might succeed, but the more fingers you use, the easier (and less painful) it will be. You can see in the image that I've got three fingers all lined up on the one string and they are all assisting in pushing it sideways across the fretboard. My ring finger is the one that's got the note under it; the middle and index are just helping with the push. With enough practice, this becomes automatic and your hand will know in advance how to organize the fingers as you're playing in order to achieve this group effort.
2. Bending is usually done on the thin strings. The thicker they get, the harder it becomes, so don't feel discouraged if you can't bend the A or even the D string. I usually confine my bending to the E and B strings.
3. Strings become 'stiffer' toward the nut and the bridge, so the best area to bend is somewhere up above the fifth fret. Again, a lot depends on the gauge of your strings, but trying to bend a string on fret 2 is a lot harder than fret 7 or 10.
4. Make sure you keep a good solid contact with the fret wire. You need to keep applying the downward pressure on the string at the same time as applying the sideways push. The point of contact needs to slide across the fretwire cleanly so that you don't choke the note off. A nice smooth action is needed.
5. Try not to bend the pitch up beyond the target note. It will take a lot of practice and listening to be able to stop the bend when the pitch reaches the target note's pitch. Being slightly flat of the desired pitch is much less disturbing than being sharp, but it will always sound best if you reach the desired note and stop.