Convert the code one file at a time. If you code base is following conventions then you will generally have one Objective-C class per file, with maybe some enumerations and protocols hitching a ride as well.

In general the approach to conversion is:

1. Create a new .swift file with the same name as the Objective-C .m file (or the .h file if no .m) Drag files around in Xcode so that the .m, .h and .swift files are next to each other.
2. Copy the Objective-C code from both the .h and the .m file into the .swift file. Consider it a framework for the conversion.
3. Convert the Objective-C code into Swift until you see no red dots or yellow triangles in Xcode.
4. Delete the old .h and .m files (they are recoverable from source code control, right?)
5. Compile and fix any introduced bridging problems.
6. Run tests and commit

Then move to the next file. Easy.