I have a 17 inch flat monitor with 1024x768 resolution.
Can you please tell me how big fonts do I put on the screen and just how far I need to be for the following: 24mm, 50mm, 70mm, 105mm
If you use the standard windows "Editor" or Excel and don't fiddle with font sizes, the letters are displayed at a 1-pixel width. That is the sharpest you can get on a monitor. So just fill up your screen with "X"s and "H"s and set your monitor to a brightness which you find "bright" but not "glaring". The black letters should still look just that: black. As an aside my monitor is not too bright, so I turn brightness all the way up to 100%. A bright monitor also makes it simpler to shoot at shorter shutter-speeds and avoid shake if you're shooting handheld (for best results though use a tripod or at least some suport for your cam).
Now on to taking the shots:
For starters just take pictures at your favorite focal lengths where the monitor just fills the viewfinder. In this case the magnification is about 1:15 meaning that the distance you need to have from your monitor is about 15xfocal-length: so for testing at 70mm your camera has to be around 1m away from the screen. Just go back and forth until the screen totally fills your view-finder. Watch-out to be perfectly perpendicular to the centre of the monitor (that's where the tripod helps, too) which you can easily controll by checking that the pic in your view-finder is as rectangular as can be - otherwise, you're slightly off-centre and have your cam tilted non-parallel to your monitor.
: As your monitor has an aspect-ratio of 4:3 and your cam an aspect-ratio of 3:2 you will not see the upper/lower borders of your monitor, when you have the left/right-borders of the monitor aligned with the left/right borders of your view-finder. But that's ok.
: It may happen, that at 24mm focal length you cannot get close enough to your monitor to fill the viewfinder (24mmx15=36cm distance). That's also not critical, just go as close as the AF of your camera allows.
Next have a close look at those pictures on your monitor at 100% magnification
. Typically you should see that at the centre the pics are sharpest and sharpness deteriorates to the corners. At least in my tests I found this revealing although at this magnification there are still approx. 13 sensor-pixels peeping at one (full-color) monitor pixel - so you're far away from the limits of sensor-resolution. Following is a 100% crop from the centre of such a pic:
You can clearly see the single pixels on the monitor. If not, check focus or alignment.
If you make two such shots, one with say f3.5 and one with f11 you should be able to see that the f11-shot is sharper than the f3.5 shot.
the centre is as sharp as the corners and there is no discernible difference between a f3.5 vs. f8 shot, your lens is certainly quite good and you have to tighten the test-procedure a bit. This is done by going further away from the monitor and repeating the shots.
Well in the first sequence of tests the distance should have been approximately 36cm for 24mm focal length, 75cm for 50mm focal length, 105cm for 70mm focal length and 160cm for 105mm focal length.
Now try for 4x the distance, that is 1,4m for 24mm, 3m for 50mm, 4m for 70mm and 6m for 105mm. The exact distance is not critical, but
if you compare two lenses at the same focal length (say your 24-105mm at 70mm and a 70-200mm at 70mm) use the same distance so that magnification is comparable between the two lenses!
At that distance you're close to 1 sensor-pixel peeping at one (full color) monitor-pixel, that being the resolution-limit of your cam. So you will certainly see a degradation in sharpness in the centre. Now that your monitor fills only 1/16 of your pic, you can only judge centre-sharpness but that can then easily be compared to the same shot from another lens.
Then you know which lens is sharper.