How does crunchyroll work?
And how can I pay for just 1 month?
I covered the basics in reply to your question about how the trial works. Here's the part about membership after the trial.
Right now when you sign up for a monthly premium membership you will billed every month until you cancel. Currently if you cancel with less than 30 days left in your membership, the cancellation takes place immediately, so you need to wait until your last day of the current membership to cancel if you don't want to lose days.
However, it appears that you could use the Gift Membership option to have a 1-month code emailed to yourself, which you could use without it automatically renewing.
As to how crunchyroll works--not sure exactly what you mean by that. The main benefits of a Premium membership are that you don't see ads during video playback, that you get access to simulcasts without having to wait a week (and in some cases are able to see older shows that regular members don't have access to), and that you get a discount when buying merchandise from the Crunchyroll Store.