Rejecting the invitation is fine, you just need to qualify for another invitation whenever you next want to join. This is done by successfully picking 10 or more pockets or by breaking into a store without using an Open spell. You'll receive a letter shortly after.
However, it's important to point out that once you choose to leave a guild, they will not accept you back.
You don't mention which guild you refer to when asking about the time taken to rank up so I'm going to assume you mean for the Dark Brotherhood, although the system is very similar for the Thieve's Guild too.
For each quest you complete in the guild, you gain reputation and each time you fail a quest, you lose reputation. The amount of reputation received is usually +5 for success and -2 for failure. There are some quests that require certain objectives to be met and these incur their own set of reputation gain or loss numbers.
To see more about the Thieve's Guild, click here and to see more about the Dark Brotherhood, click here.
Hope this helps and don't forget to search the Uesp wiki first!
