As with so many things when it comes to assisting elderly parents, there is a "right" way to do this and a "wrong" way. I put "wrong" in quotes because the method I consider to be "wrong" is not necessarily illegal; it's just less than optimal.
Just like it is a bad idea to add yourself (you being the adult child, friend or other helper) to the elder's bank accounts as a co-owner, it is a bad idea to add yourself to the elder's credit card accounts as an "authorized user". That method "works", but there's a downside, which is the elder's credit card account will now appear on YOUR credit report. If they have a high balance compared to the available credit, or just a high balance in general, or a poor payment history, these things could negatively affect YOUR credit score.
The right way to do this (just as with bank accounts) is to obtain a power of attorney from the elder appointing you as his or her attorney in fact. Send the power of attorney to the credit card company so that they will recognize you as as the authorized agent of the user, and you can set up online access, but you won't be personally liable for paying the credit card, and it should not appear on your credit report. If it does appear on your credit report, you will have the grounds and the documetation to object to the credit reporting agencies and get it removed from your credit report.