Hi, just on my way to work but will try to answer on my iPhone.
It depends what you want your projected outcome to be. If you want Photoshop to Manage Color & you’re happy with your media type=paper, then you’d pick that.
Usually Photoshop determines automatically what the Document Profile is, ie sRGB, Adobe RGB etc. You then select your paper icc profile as outlined earlier. This will give you a fairly accurate rendition of what you see on your screen IF you have calibrated your monitor correctly.
However, if you want to apply a different treatment & want to experiment with fully manual options in the printer driver, then select Printer Manages Color in Photoshop. You’ll then see that Photoshop shows your particular printer’s driver profile. You cannot change this (that’s why it’s greyed out) unless you change the printer you’re using for that print job.
In the printer driver settings you’ll then select Printer Model (or whatever printer). You can then change from ColorSync to whatever paper/media setting you want. Then in the driver’s colour option you will find you CAN alter the colour settings with the sliders. This will affect the colours of your print depending on what settings you’ve chosen.
Remember, unless you’ve specifically changed the Document Profile (Edit>Assign Profile) inside Photoshop for some reason, for example, your raw file from Adobe RGB to Pro Photo, you don’t need to alter it. Photoshop will assign the correct Document Profile automatically.
The Document Profile option ONLY concerns the colour property of the digital file, it is not the Paper Profile which is solely a printer requirement, ie it is an ICC profile.
Edit>Assign Profile has nothing to do with printer setup. It’s only for Photoshop to know what kind of document it’s looking at. Normally there is no need to change it.
Hope this helps? I’m doing this from memory as on public transport so hope I’m making sense for you! Alan
Sent from my iPhone
D Fosse is totally correct & succinctly puts it.
Just to underline what's been said: you never need to change the Document Profile in Photoshop: it's sRGB or Adobe RGB or ProPhoto. The one thing I personally think that could have a better name is "Document Profile". I think Adobe should call it a Digital Profile. The word Document is all too easily read as pertaining to a document, as in a paper document, hence the confusion with Paper Profiles / ICC profiles. A Digital Profile to me would read more clearly as what it is: digital information that characterises the colour basis of that file. That is what Photoshop is asking here. But it pretty much always reads the file correctly for you.
Adobe's terminology can sometimes be confusing, for new as well as experienced users.
And don't Edit>Assign a file in Photoshop, it will muck you about. Unless, as has been stated, there are special reasons for doing so.
The whole point of colour management is to produce CONSISTENCY in image & printing. So things can resemble what you see in your calibrated monitor. Or to put it a better way so that your monitor more closely matches your printer's output. But if you want to experiment - for the reason the original poster asks about --
"...when in the process does the user get the opportunity of making the changes to the image file necessary to bring it back in line with the desired effect?"
It's generally way too late to do this at the printing stage - although some modifications can be made when you select Printer Manages Color. The real place to be creative is when you are working in Camera Raw inside Photoshop, or special effects again in Photoshop, or in the Develop Module in Lightroom where you can then print from the Print module, or from software like Qimage One. There is plenty of software out there. Sending your file to be printed is the last (mainly technical) stage of the process.