You can charge the battery right in the vehicle, as long as it is not a refillable, wet lead-acid battery. I recommend bringing those inside, and charging periodically on the shelf. They will go dry otherwise, and continuous charging sulfates them sooner. The Spyder can be charged continuously on the machine, with the right charger, as it is a sealed battery.
I have numerous battery chargers, and have tried many others over the last 45 years. A low amperage "trickle charger" for automotive use is generally too strong for motorcycle batteries. It used to be all we could get, but shortens the life of the battery. My favorites are the Battery Tender, Battery Tender Jr., Accumate, and Optimate. The Optimate has the best maintenance cycle, but does not seem to do any better in real life than the others, IMO. It does have a desulfating routine for marginal batteries, and some diagnostic indicators. Our Spyder is on one this year because that was what was left after I hooked everything else up. One BMW is on a Battery Tender Jr., and one is on an Accumate right now. The rest get periodic charging in the basement with another Accumate, because mine will do both six and twelve volt batteries. A necessity for my vintage bikes. I have spare Battery Tender Jrs. at this time, but they always worked fairly well. They charge a bit slower than the full-fledged Battery Tender. All the units I mentioned have a "maintenance" mode, but only the Optimate has a true maintainer function, with automatic, periodic charging cycles. Don't use the higher amerage automotive "battery maintaners". They are too strong for a bike battery over the long haul. I have used them on a one time basis in a pinch.
There are several ways to hook up your charger. The alligator clips can just be clamped top the terminals temporarily, the harness that comes with the unit can be attached to the battery, then accessed and plugged in to the charger when you need it, or you can install a continuously powered automotive (cigarette) or Powerlet outlet, like I did, and plug in the charger with the proper adapter. Be aware that the Battery Tender units do not take the same connector as the Accumate or Optimate. One harness won't serve the other type of charger.
-Scotty