Nishio
One technique known as "Nishio" means to find a cell with just a couple of candidates, and to pick one of the candidates. If you work through from that point, and it turns out to be solvable and a valid grid, then great, you guessed right! If your guess was wrong, maybe it would show itself up within just a couple more moves, maybe it would take right until the very end before the last number was incompatible... Do you feel lucky? Some people will try just a few moves, before deleting them and trying another for speed.
Finding an incompatibility quickly means you can delete that option, and know that the other choice was correct. In some ways, picking the right number is less lucky, because you won't be sure it was right until you've gone on to solve the entire grid!
Here's a puzzle with a cell highlighted:
(258)49(23)(38)61
(23)698(13)(1237)(34)(35)(3457)
(38)4156(37)(389)2(379)
(45)1(458)(39)2(358)7(3589)6
(26)73(69)4(568)1(589)(259)
9(58)(26)(136)7(13568)(23)4(235)
(45)3(457)(267)89(246)1(24)
(68)9(68)(123)(13)457(23)
12(47)(367)5(36)(3469)(39)8
)
(258)49(i2s3)(i3s8)61
(i2s3)698(13)(1s23s7)(s3i4)(s3i5)(s3s4s5i7)
(i3s8)4156(s3i7)(s3i8s9)2(s3s7i9)
(i4s5)1(s4s5i8)(39)2(35s8)7(35s89)6
(s2i6)73(s6i9)4(5s68)1(58s9)(i2s5s9)
9(i5s8)(i2s6)(136)7(13s568)(s23)4(s2i3s5)
(45)3(457)(267)89(246)1(24)
(s6i8)9(s6i8)(123)(13)457(23)
12(47)(367)5(36)(3469)(39)8
)
Lets choose the value 8 for that cell, and follow through the values it would force into the nearby cells and so on. Without too much effort we reach this, crossing out the candidates that aren't possible, and highlighting in blue the single candidates that would become the new cell contents if we followed the results of that 8.
(There are still a few more that could be crossed out - but this is far enough for the example.)
(258)49(i2s3)(i3s8)61
(i2s3)698(13)(1s23s7)(s3i4)(s3i5)(s3s4s5i7)
(i3s8)4156(s3i7)(s3i8s9)2(s3s7i9)
(i4s5)1(s4s5i8)(39)2(35s8)7(35s89)6
(s2i6)73(s6i9)4(5s68)1(58s9)W(i2s5s9)
9(i5s8)(i2s6)(136)7(13s568)(s23)4W(s2i3s5)
(45)3(457)(267)89(246)1(24)
(s6i8)9(s6i8)(123)(13)457D(23)
12(47)(367)5(36)(3469)(39)8
)
There are lots of cells you can see with blue entries, which would be the single candidates for those cells - but have a look at the two highlighted cells on the far right column - which would be a 2 and a 3.
Can you see what effect these two would have on the cell marked in grey?
Because that 8 would lead to the grey cell having no possible candidates, you can be sure that 8 cannot possibly be the value in the original highlighted cell, so you can safely choose the 5 as the correct option.
Is it always that hard?
Not always - but often! Sometimes you'll see the contradiction (error) within just a couple of placements, sometimes you'll get nearly to the end.
It is worth reminding here that Nishio only works by finding a contradiction, from which you know to pick the other option. Only if it actually leads you to complete the grid can you be sure that you had the right option to begin with. If you can only fill in a few cells, and there are still more to determine, then it isn't enough for you to be sure. A positive isn't proof, but a negative is a disproof!
Tips
Try picking a value for a cell which looks like it will immediately force lots of other values. That way you can be sure that you'll get good reward for your effort if it does turn out to have a contradiction.
Try picking three or four values and just working out a short chain from each. If you don't find one quickly, then move on and try another. There's often a very short chain nearby, and its worth a quick search to find it before you start the much longer and more meticulous searches.
An overlay (tracing paper or a computer equivalent) really helps you to try out various chains without you making a complete mess of your original!