Stabilising a wine means making it stable biologocal and chemical.
When high temperatures arise some proteins might precipitate (did I spell that right ???) out. The wine then gets hazy.
So test the wine by taking a sample and heat it. If it gets hazy you will have to fine it with fining aids.
Next is cold stabilising.
A wine with a lot of tartaric acid might throw chrystals when the
wine is chilled. The chrystals are parts of tartaric acid at (again spelled) precipitate out of the wine.
So the wine is chilled then look if any chrystals form and if they do rack the wine.
The racked wine is then cold stabilised.
Last is to indeed add sulphite and sorbate.
Sorbate prevents any living yeast cells to multiply (reproduce). And sulphite helps kill molds, bacteria and helps keeping oxygen in control to prevent the wine to oxydise.
There is a lot of free literature around on web-sites.
If you read my wine-weblog you will find in the right column on my log a list of free downloadable winebooks.
They might shed some more light on all these complicated matters.
Luc