All depends on what information is in the ATC system.
Many people would also argue that it's not upgrading, it's just changing category.
If you filed a flight with an upgrade/change cat point enroute, too easy if not a little harder; assuming it got through the filtering process at the ATC end.
You need to submit details if you are VFR without a plan in the system (sometimes even if you planned VFR flights don't always make it through the filters); before requesting the upgrade, preferably. If you need it immediately then it's a little harder, depending on airspace too it could even be quite 'ugly' if there are other IFRs about; ie Class E and getting an immediate upgrade.
Technique: have a good listen on the freq before jumping in, is it reasonable to make the controller work harder, even briefly. Any ATC can submit details into TAAATS, so if you are close to a VHF boundary have a search around for the quietest freq.
"XX Centre, VH-ABC, VFR C172, IFR Details"; expect them to say standby as they grab a pen and paper and do a workload assessment.
The details we need are, in no particular order:
Callsign, type, ADEP (helps at our end), ADES, requested level, current location and route to be flown, anything else pertinent.
If you can do that 5 minutes before you need it, it helps a lot regarding workload; if you can do it 10mins before on a flightwatch freq, it helps even more.
Flightwatch don't have a TAAATS feed, and will submit details to TAAATS via messaging so it takes a little longer and sometimes still won't get through the filters, but it is there somewhere, just not at the ATC console. If you submit via flightwatch, let us know, then we know where to look if we can't find the details.