There are several references to tithes and offerings in the Tanach. What are some of the Jewish laws for donations (whether a tithe or feeding the hungry)? What are the laws? Where can I read specific passages of these laws?

It's impossible in a short answer to cover all the details, though one should distinguish three different issues you mentioned; tithing, voluntary offerings and Tzedakah – Charity. Tithing (Trumah and Ma'aser), is a commandment to do with crops; one has to tithe his crops about two percent to the Cohen, ten percent to the Levite, in some years ten percent more to the poor etc. Voluntary offerings can be donated to the Beit Mikdash whenever a man feels the need to; in fact any donation can be donated to the Temple. In addition to that there is a mitzvah to give Tzedakah to the poor and needy, food, money or clothes, or even better - giving him a loan to start a business. To see more try Kitzur Shulchan Aruch chapter 34 for the laws about Tzedakah. For the laws of offerings and tithing you can find in length in the Rambam.