I just felt a serious need for lowering my guitar action as I think I was unable to play faster because of higher action... Thus I lowered the string saddle a bit..and then tightened the truss rod because the string were buzzing at high frets...Bt I ain't helped much so I loosened it as before... Then when I checked my string intonation it was messed up...changing saddle position I.e.bringing them back or forth is not helping at all..I don't want to raise the strings as I am preferring as low as the action can go..looking forward for solutions.. Thanx n pardon for English(if there are mistakes)..
The truss rod is there to counter the bowing (just like a bow and arrow) of the neck. Generally, there should be just a tiny bit of bowing, barely perceptible. If you were to lay a straight flat object along the frets, you could just about slide a piece of paper under the middle of it. The easiest way to get intonation correct that I know of (and not necessarily the best) is to use a tuner. first of all get the open string to correct pitch as precisely as possible, then play the 12th fret. If it is sharp, the string is too short and you need to move the saddle towards the bridge a little bit, if flat do the opposite. retune again and try the 12th fret and slowly adjust. Changing the intonation on one string may affect other strings, so you may have to repeat the process many times. It's good to learn this yourself on an inexpensive instrument.
If you have an expensive guitar and you don't really feel confident doing this, I would recommend taking it to luthier or instore guitar tech. A good setup is a good investment. At face value it might not seem as exciting as a new pedal but a cheap guitar well set up can feel and sound better than a badly set up expensive guitar.
Finally, action and string gauge can be a trade off. You can have a low action with heavier strings because they buzz less, or a slightly higher action with lighter gauge strings. You may find a change of string gauge more to you liking than the lowest action possible.
Edited to correct the mistake mentioned in comment below.