After you have run a a filter on your Contacts or Giving tab, you can click the select all box above your results to make the Export button selectable!
You can then click Export on the top right for Contacts, or click Bulk Actions and then Export in the top left for Giving, and in the resulting popup, you will select the fields you want to export.
These fields you select will be the column headers on your Excel sheet and the corresponding data will populate in these columns. The fields on the right hand side will appear as the column headers.
After you choose the fields you want exported and click Export! You will get a an email with the spreadsheet attached. (This email might take a few moments to send because it is pulling a lot of data and that takes time!)
The file will also appear in your Exports section. Go To Settings > Exports.