I've never had one in a New Beetle so I can't tell you specifically, but I have had several cars with trunk mounted batteries so I can give you some generic info.
Basically all you need is a longer cable and a mount of some sort. Once you figure out where you want to mount the battery and get your mount sorted you will have to run a cable front to rear. Probably the best place would be under the car, just make sure it's well protected from damage. Alternatively, you could run it inside along the tunnel (probably under the carpet) and through the firewall. Of course you will need the proper size grommets when running through metal panels, well sealed to keep out water, fumes, etc. Another option is a bulkhead connector.
Once the cable is run front to rear, I suppose you would want to make some sort of mount for the fuse box that sits on top of the battery. I would also suggest a case for the battery. Many places sell complete kits to relocate batteries.
I would also suggest an AGM battery, just to reduce the chance of spillage. Venting is a issue, I'm not going to say you need it, but be aware. Some claim it's unnecessary, others claim you will die without it. I'll just say VW (and others) made millions of cars with batteries under the rear seat without vents and you didn't see dead drivers all over the road back in the day. However, if your battery has provisions for a vent tube I would suggest you run a tube outside the passenger compartment, just to be on the safe side.
Finally, it may be worth considering a smaller alternative battery up front if it would give you enough room. Braille Batteries are one manufacturer, I'm sure there are others. Not cheap and I can't say how they would hold up, but certainly less hassle that relocating the battery.