I’m trying to disassemble my computer and the chart below is from the manual.
I cannot find any specific M2x1.9, M2x2.5 and such screwdrivers online at any store. Please help.
"M2" is the type of screw and "x1.9" means "by 1.9(mm)" so it is an M2 sized screw that has 1.9mm of thread (the spiral section).
M2 specifies the "nominal" thread diameter as 2 millimeters. In practice the actual diameter is slightly smaller than 2mm as sharp tips of the thread are not a desirable feature and can cause mechanical problems.
What type of screwdriver you need depends entirely on what type of head the screw actually has. There are Pozi, Phillips and flat head types among others. At a quick glance a PZ0 (Pozi 0) is most likely "correct" for M2 Pozidrive screws, but you should figure out the specific type (Pozi or Philips) and use the correct bit.
You should just get a generic "precision" or "computer" screwdriver set. It will likely have most types of screwdriver in the most common sizes you will need and you can use the right screw head.
On a laptop computer, you'll almost never find any flat-head screws. They are typically Phillips, occasionally Pozidriv or Torx. Various 'security' screw heads also exist, though those are more specialty and not often used in user-serviceable laptops.
You'll need to look at the screw heads to distinguish between them. Images from Wikipedia (public domain by Inductiveload):
Phillips (PH):
Pozidriv (PZ):
Torx:
Note that Pozidriv has the extra diagonal cutouts.
You will almost certainly strip the head, and have a horrible time both taking it out and putting it back in. Phillips screwdrivers on a Pozidriv screw aren't great either, but are a little less likely to cause damage if you're careful.
Beyond that, there's also the size to worry about - these go from 000, 00, 0, 1, 2, 3.
You will want a screwdriver set that includes PH1, PH0 at least, and preferably the PZ equivalents too. Typically M2 screws are PH0/PZ0 heads, while M2.5 and bigger screws will use PH1/PZ1 (and then on to 2 and 3 sizes, but you won't find them on a laptop -- maybe 2 on a desktop).
Your driver should fit all the way down to the bottom of the channel in the screw head. If it does not, it's too big, or the wrong type. It should also fill out at least the width of the channels, such that there is little to no space to turn the driver in either direction without also turning the screw. If it does not, it's too small.