How do I read a sequence logo?
A very clear description is given in Wikipedia.

The starting point is an alignment for the region under investigation.

A. Basically, to get the height of the stack of letters for every position one has to calculate the degree of certainty about the residue (= degree of conservation) at this position in the sequences belonging to this class. I'll explain what it means:

The key parameter in this context is information. 1 bit of information can be understood as the amount "knowledge" you get when receiving an answer to one yes/no question.

Let's say we have equal proportions of all four bases at a certain position in a set of DNA sequences. To "guess" a base at this position in some sequence we have to ask two binary questions. For example: "is it Pyrimidine?" If 'yes' we'd ask "is it 'T'?" Otherwise: "is it G?". So, when the frequencies are equal we can get 2 bits of information from one observation of a base at this position in a sequence.

If the frequencies are distorted, we already have some ideas about the bases when coming to an individual observation. If we already know, say, that we have just G and A at this position with ratio of 1:1, we can just ask "is it G?", so we get clearly 1 bit. When the ratios are not even (or when the number of alternative states is not 2n), the analogy with the questions becomes much less clear and we have to resort to the very simple formula for Shannon entropy. Intuition and brief inspection of this formula would bring you the idea, that when the ratios of the residues are biased, we always have less information than for the case of equal frequencies (2 in the case of DNA).

Now to estimate the "the degree of certainty" we simply calculate the information based on the observed frequencies of different residues at this position and subtract it from the theoretical maximum (again: 2 in the case of DNA):

certainty = maximal information possible - actual information

This value defines the height of a stack of letters at each position.

The maximum value (2 bits) would be observed when we always have the same base, because "actual information" would be zero (there is no need to ask questions - we "know" the answer anycase). The minimum (0 bits) is when we have no idea about the base. One bit would be obtained if we had, say, just two equally frequent bases. And, for example, the value of 0.6 would be observed if you had, e.g. 68.5% of the time the same base A and in all other case C, G or T with equal frequencies of 10.5%.

B. As you probably already know: the proportions of all alternative bases are shown as relative heights of individual letters.