Angela, I'm sorry to hear about your guinea pig.
You could call your vet - on the weekend you will likely get the answering service, but they should be able to tell you what to do.
Or, many Gemeinden have a Tierkadaver collection point; this (sorry to be insensitive or blunt) is a public incinerator. Check your Gemeinde website - the collection point is usually listed.
You can arrange for a cremation at a Tierkrematorium, if you so choose. There is one in Duggingen: http://www.kleintier-krematorium.ch/sofindensieuns.html
Or, there is a pet cemetery in Läufelfingen: http://www.tier-friedhof.ch/48/Dienstleistungen.html
Both these options may be expensive. (I think both of these are out Baselland way - my geography is not what is should be...)
And yes, you may bury a small animal; often one does so and then plants something to remember your pet by - perhaps a rose bush, or a tree - above the grave. Obviously if the garden is shared you'd need to ask the neighbor first.
Again, I'm very sorry to hear your sad news.