I would say the steps you need to take in the scenario you describe are 100% dependent on the development environment and tools you have set up.
Using Perforce for source code version control, we have set up a branching system where the releases are separate from development work and all development branches stem from a single "acceptance" branch. Each branch is used for a single issue, or for a set of very closely related issues. No other issues can be worked on in a branch until the changes have been integrated up to the acceptance branch.
Yes, it does mean we have a lot of branches. Yes, we do a lot of syncing (acceptance down to a work branch) and integrating (work branch up to acceptance). But its worth is incalculable when it comes to easily switching from one task to another, going back to a test-built, spotting two issues biting each other, etc.
After development has done its thing (including their own tests), an issue is tested by the QA team. First in isolation in its own branch. After that is is integrated into the acceptance branch and a regression test is done to find any problems with independent issues biting each other. When all issues for a release have thus been integrated into acceptance, a full regression and new functionality test is executed by the QA team.
So, the acceptance branch is always the "latest" state of development for the app.
In this set up the scenario you describe would play out as:
Leave my current task as it is, possibly check in any outstanding changes so as not to lose them when my computer crashes. If that means breaking a daily build of that branch, I wouldn't check in, unless it is easy to fix the compile errors. (Please note that we have many apps in our application suite and while my changes may compile in the app I am working on, they may still break the compilation of other apps in our suite) Our rule is: each submit may break functionality, but must not break the build process.
Find an "empty" branch - a branch that is not currently being used for any development work, or, if all branches are taken, create a new one.
Force sync the acceptance branch and the selected work branch so my machine is guaranteed to have the latest state for both branches.
Synchronize (forced if necessary) the latest state of the acceptance branch to the work branch, so the selected work branch is the same as the acceptance branch.
Open up that branch's application suite in the IDE, debug and solve. Submit to the work branch.
Tell QA to have a look at it in the work branch. If they are satisfied with it, integrate the changes up to acceptance so they can continue their test.
Switch the IDE back to work on the application suite in the branch I was working on before.
Rinse and repeat.