How does a salt get chosen? I feel like I am missing some information regarding salting.  How does one choose the salt? If you reuse the same salt for all passwords, can it just be figured out and then used in conjunction with normal brute-forcing.  And what are the common ways to generate the salt?
Salt is not secret. This is the open part of the encrypted data. It should be open to decrypt the data.

Reusing the salt is not good. The whole purpose of salt is to prevent usage of rainbow table. If an attacker has descrypted one text, it should not be easy to use it for other texts. Where as if you reuse the same salt for many texts, it may make sense for the attacker to create a rainbow table because he can then decrypt your multiple texts via the same rainbow table.

To your question, how salt is chosen: As @Swashbuckler said, it should be random. Important: Not once random, but it should be randomly generated for each your text or password.