Hey Dougal,
Let's start at the top left and work our way around clockwise:
1) We see that there are two chiral carbons here. The carbon with the -OH and the carbon with the -CH3. Now, it might be a little confusing since they are in a ring, which is fine. If we look at the carbon with the -OH. We see that it has an OH, a H and then two possible paths around the ring. If we look at those two paths, we see that they are indeed different. If we go around the ring to the left, we encounter a CH2-CH2-CH2-CH(CH3), but if we go around the right, we encounter CH(CH3)-CH2-CH2-CH2. Even though it is in a ring, we see that the environments as we go around the ring are different depending on the direction, hence two "different" groups, in addition to the H and OH. This same process can be carried out for the carbon with the -CH3 on it.
2) This is much the same thing. The only difference is that we only have 1 chiral center, namely the carbon with the -CH3. See if after the previous explanation this one makes more sense.
3) This one is analogous to the first one, only with a carbon cut out of the middle
4) This one is a little different. We initially suspect that the carbon with the CH3 and OH groups might be chiral. However, if we trace the path around the ring for that carbon, we'll notice that it is actually symmetrical. Because of this symmetry, the carbon lacks chirality, because it lacks 4 distinct substituents.
Inductive effects are the electronegative effects that adjacent atoms have on each other. For example, if we have chloroform, CHCl3, we can see that the chlorines have an inductive effect on the molecule as they pull electron density towards themselves. For a more applicable (albeit slightly more advanced example), this trend is probably most noticeable when looking at pKa values. If we look at acetic acid CH3COOH, we see that it has a pKa of about 4.7, indicating it is fairly acidic. However, if we look at something like Trichloroacetic acid, CCl3COOH, we see that it has a pKa of only 0.7. This can be explained by the strong inductive (electron withdrawing) that the chlorines have on the molecule. The chlorines pull electron density away from the rest of the molecule making the hydrogen even more acidic.