At your local big box do-it-yourself store, or at other local hardware retailers, you can find a 3/4" sink/hose adapter. I believe it cost me about $4. It attaches to your sink faucet and has threads that a standard hose can be attached to. Then run a food-grade hose from the sink to the barrels. We bought RV water hoses (from Wal-Mart) to use, but any food grade hose will work.
In our case, the barrels are in the basement. So I needed about 100' of hose, and luckily most of it was flowing downstairs, so water pressure was not an issue. You insert the hose into the top opening and fill the water until it's about to start coming out. Add any conditioner/cleaner you feel is necessary (Not going to get into that as that's a whole other discussion), and then replace the cap and tighten.
|Filling a barrel. The bottom bib is obvious closed.|
In the image above, you can see the water stain on the floor. That's from screwing in a hose bib too tight and cracking the bung cap. I didn't realize it was leaking until some time later. Be careful installing the hose bib to avoid the same problem.