How do I get my solution in Visual Studio back online in TFS?

Rename the solution's corresponding .SUO file. The SUO file contains the TFS status (online/offline), amongst a host of other goodies.

Do this only if the "right-click on the solution name right at the top of the Solution Explorer and select the Go Online option" fails (because e.g. you installed VS2015 preview).

Go to File > Source Control > Go Online, select the files you changed, and finish the process.

I searched for the solution online and found this solution but wasn't too keen on the registry change.

I found a better way: right-click on the solution name right at the top of the Solution Explorer and select the Go Online option. Clicking this allowed me to select the files that had been changed when I was offline and make the solution online again.

After finding the solution, I found the following msdn forum thread which confirmed the above.