328 support is now built-in and standard with the version 13 release to the IDE.
Prior to 13 there were modified files that had to be changed to allow the 328 to work with the IDE such that it would recognize the additional memory sizes of this chip. The vendor I bought my 328 from several months ago had a link to the modifications needed to work with Version 11 of the IDE.
The differences between the 328 and the 168 are pretty minor and you should see no differences except for having double the programming space!
I also have a 40 pin 644P AVR chip that has double again the memory space of the 328 (64K). It does not yet have built in support of the official IDE yet but the vendor provided links to files and instructions for modifying version 12 of the IDE and that has worked fine for me. I went ahead and applied the same changes to the version 13 IDE (as an experiment) and so far have seen no problems using the 644P with version 13. The 644P is a little trickier to use as the digital pins numbers and what functions they perform are different then the 168/328 chips, but other then having to change pin numbers in some existing sketches, it has worked well. The 644P is the ultimate bread-boarding chip if your board is large enough.
Edit: PS, you may have to edit the boards.txt file to change the baud rate that the bootloader in your 328 uses to match. I did have to make that one minor change in version 13. I assume vendors of preloaded 328 will eventially change their installed bootloaders to the new IDE’s default baud rate now that the IDE has native support for the 328.