Many organizations issue all of their tax receipts to donors (which are also called contribution statements in the USA) after the year-end, though it is also possible to issue them regularly during the year. See Receipts for details.
For Canada, the CRA (Canada Revenue Agency) recommends that all receipts for the prior year be sent to donors by the end of February. For the USA, the IRS (Internal Revenue Service) requires receipts to be sent out by the end of January.
You may want to use various reports to review your data before issuing the receipts. Helpful built-in reports include All Donations, Receipted Donations, Unreceipted Donations, and Non-Receiptable Donations. The last three of those, between them, include each donation in one and only of the three reports.
If your organization is a church and you use envelope numbers, you may also want to reassign them for the new year before the year-end, in order to be able to order envelope boxes. Even if your donors keep the same envelope number from year to year, to see them in the new year you need to take action! See Assigning or Reassigning Envelope Numbers for details.
For any users who previously used Classic versions of DONATION (such as Standard or OnDemand), in DONATION Online there is nothing you have to do to start entering donations for a new year, and there is no action required to switch between working years (except possibly the reassigning envelope numbers as mentioned in the previous paragraph).