How do I replace the bulbs on the SwissGear rechargeable lantern?

Unfortunately nowhere. If you look by the charging port, there is often a sticker that shows volts, amps and polarity. With that you can buy from Amazon or eBay.

https://www.google.com/search?q=SwissGear+lantern+SG66301+AC+Adapter

..

will the main light come on when plugged in? it might just need a new bulb. if so it might be a dead battery

There are several different models of the Swiss Gear rechargeable lantern. On most though, you can remove the top portion of the lantern and check the lighting element inside. In most cases the elements can be removed and replaced. I have a dual filament lantern and from experience I know that every so often you may have to go buy a replacement light piece. If the lantern has been bumped or even just strapped to the outside of the pack while walking, it's possible for those elements to become loose and need repositioning or replacement so do check that. I'm sure that it should be unlikely your charger is malfunctioning unless you left it plugged in for some very extended period of time, in which case I would say the light would be more likely to burn out. But definitely try that and if that doesn't work the battery pack on the lantern itself may have an issue in which case you can always get a replacement.

The adapter need to match the charge voltage requirements of the battery in the Swissgear lantern.
This voltage maybe written on a label on the lantern.
i suggest go to the shop where you purchased the lantern for the charge adapter.

I just bought a retro rechargeable sealed battery,recently. I charged it for 18 hours,the lights all worked,but I don't remember the green light comming on.i put the lantern away for 3 months or so.i decided to check the the battery light out first week of june, the light was there,then I said let me charge it up again, I never seen any green light come on showing it was fully charged. I took the battery out and checked the wires to see if there was a break. None that I could tell. After you take the battery out ,there is another section square that covers where the bulb is located,but I didn't touch that part yet. Stuck" on this one. Help"

I think the switch can be replaced. Here on amazon you can purchase parts: Amazon com Coleman retro parts I hope this helped. Cheers

just read the charging instructions. Charge for 16-18 hours. If stored for more than 6 months recharge for the full 16 hours. Do not leave the lantern on after the battery has stopped, has overdischarging the battery can cause problems in recharging to a full charge. If this does happen, switch lantern to off and recharge for 40 hours.YES 40 hours. Only the LED is the only light to be used while charging. If you hane the other light on hi or low the battery does not charge.

Hope this helps

Check the battery with a volt meter to make sure you have the correct voltage. If not, replace battery. If correct voltage, bypass switch to determine if it is good or not. If not, replace. There really isn't much to go wrong on the lanterns except the bulb or battery.

You can find the bulbs you need at this link; http://www.bulbs.com/eSpec.aspx?ID=14393&Ref=Light+Bulbs%2c+Ballasts%2c+Fixtures+and+More&RefId=0

I don't know how to solve your problem but, the three lights mean this:
Red LED light indicates the battery is being charged
Green LED light indicates that the battery is fully charged
Amber LED light incidates that the battery power level is low - the battery needs recharge.
Do not recharge you battery over 24 hours.