Selectively summing/counting records is a common question asked in the forum. See this thread for some ideas on how you can get the totals/counts that you need: Sum_Calculation based on condition
In addition to the methods described there, ExecuteSQL can be used in FileMaker 12 to return such totals or counts.
I want to be able to create a report for each donor for each year, so I need to not print reports for donors who didn't give in a particular year and I only want the records from the proper year to show up in the yearly statements for donors who did give in that year.
Set up a summary report layout based on your donations table instead of your donors table. Set it up in list view and put in a sub summary layout part "when sorted by" Donor ID and put the fields you need from Donors in this layout part. You can then perform a find for all donations in a specific year and you will get the results you have described in your post. Summary fields can be used to show total donation amounts or total number of donations, etc. Be sure to sort such a found set of records by the field specified as the "when sorted by" field for your sub summary layout part or the sub summary layout part will not be visible.
See this thread for a tutorial on summary reports with summary fields and sub summary layout parts: Creating Filemaker Pro summary reports--Tutorial
I tried option 1 on the link you sent and it worked perfectly! Thank you so much. It will take a while, but I think I'm beginning to understand more of the basic way that FM works.