Computer Science: Regular languages, Regular expressions, and Finite Automata

I do not understand how to do any of these problems. My professor has given us the answers. Please provide an extremely detailed dumbed down explanation so I can understand how to do these type of problems. If there are other solutions, please explain. Thanks

1a) L is the language of odd length strings of zeroes. Give a regex for L.

Answer: 0(00)*

1b) L is the language of all strings over alphabet {0,1} where every 1 has an adjacent 1.

Answer: (0 | 111*)* or (0|11⁺)*

1c) L is the language of odd decimal integers greater than 0. Give a regex for L.

Answer: [1-9][0-9]* (1|3|5|7|9)|1|3|5|7|9