What is cryptanalysis?
Cryptanalysis is the study of reading encrypted messages without being given the key. Cryptography builds ciphers and cryptanalysis looks for their weak points. The oldest known description of frequency analysis, one of its basic methods, comes from the Arab scholar Al-Kindi in the 9th century.
Which method fits which cipher
Caesar and ROT13
The English alphabet allows only 25 shifts, so a brute force attack takes seconds. The solver runs it for you and shows every result. ROT13 and Atbash have no key at all: once you know which one it is, you can simply read the message.
Substitution ciphers
A shuffled alphabet has far too many keys to try, but each letter keeps the same disguise throughout the text. Frequency analysis shows which letters appear most often, and pattern recognition helps you confirm a guess. You need a fairly long text, because a sentence or two rarely gives a clear picture.
Vigenère
A keyword spreads each letter over several shifts, which flattens the counts. Classic attacks first work out the length of the key and then treat each position as its own Caesar cipher. This site has no tool that does that automatically, but you can test a guessed key in the Vigenère tool.
Where these methods stop
All of this relies on letter patterns surviving in the ciphertext. Modern encryption such as AES hides those patterns, so none of these methods will open an encrypted file or a password-protected archive.