This is where GitHub Desktop falls short - to resolve conflicts, you're probably going to have to use the command line shell at some point. This page discusses the issue well, but is aimed at people who don't use a GUI client at all. It's still worth a read to get an understanding of the issues, and its diagrams are very good.
-Below is some guidance for resolving conflicts using GfW and the shell where necessary.
+Below is some guidance for resolving conflicts using GitHub Desktop and the shell where necessary.
In the shell, enter git add <file> to mark the file you manually merged as resolved. Once all the unmerged paths have been resolved, enter git rebase --continue to finish the merge. You can now close the shell window.
Back in the GfW window, click the "sync" button to update the online repository with your merged revision. You're done!
+Back in the GitHub Desktop window, click the "sync" button to update the online repository with your merged revision. You're done!