How exactly would someone attempt to analyse ciphertext produced by popular encryption products such as Truecrypt/PGP?
From the perspective of someone who is a non-cryptographer but runs penetration tests against, well, anything really, there is a very simplistic answer that is generally correct in the real world:

Assuming the implementation of the encryption algorithm is not flawed (I know, not always a good assumption, but the common open source tools get a lot of peer review so it is an assumption I use) and a strong algorithm is used with a strong passphrase or shared secret, the reality is that breaking such a system is usually successful through misconfiguration or lax procedures on the part of operators.

This may lead to finding a copy of a passphrase on paper, in shared memory, in a backup, through a keylogger or even used for something else with weak password protection. So a real world attacker will usually take the easy route and look for wetware failure.

A strong passphrase and strong algorithm, by their very nature, are used to make the average time for a brute force attack beyond any useful time (caveat - the tool could get it on the first try, which is why we use averages, but as @Thomas says - you could win the lottery this week. Odds are just very very low!)