With recurring payments, you have a few options regarding start and end dates:
The default setting is Start Date: Today's date and End Date: Ongoing. This is typically the ideal setting for recurring donations
When the Start Date is set to "Today's Date" and the End Date is set to "Ongoing," for recurring payment the first payment is charged at the time of the transaction, and subsequent payments are scheduled to be charged based on the initial transaction date and the frequency the supporter chose. For example, a donor starting a recurring donation on January 5th will be next charged on February 5th if monthly, on April 5th if quarterly, or the following year's January 5th if annually. The donor's automated receipt will indicate this information, as well as provide a link for them to change their recurring subscription, such as the date on which their payment recurs. They can also use this link to cancel their donation. Since this is set to ongoing, this donation will recur indefinitely until either the donor or your organization cancels the donation manually
Alternatively, you can set a start date. You can pick the date for all recurring payments per frequency (useful for memberships), or you can give each supporter the option to pick their desired start date during their transaction.
Another option is to set an end date, or to have the system stop charging after a set number of payments have been made (ideal for setting up installments).
If you choose "On a set date" or "After a set number of payments," you then have the option to set the target date/target number of payments in these settings, or allow each supporter to choose for themselves.
If you let your supporter choose their own settings, here's what it looks like on the front end:
These settings can be set per recurring payment frequency (monthly, quarterly, annually), and you can find them by going to Campaigns > Edit This Campaign > Tool Settings > Donations/Payment > Monthly Recurring Donations/Payments.