Welcome to AO Gaz
Not too familiar with the 2.0JTS engine, but general procedure is:
Buy the oil stated for use in the hand book, It will probably say to use seliena(sp?) from an Alfa dealer but if you want to have any money left after, a good quality equivilant from a motor shop or Halfords will do.
Also get a new filter from a motor factor or someone like AlfaShop.
Basically, run the car up to temp, then allow to sit for maybe 30-60mins, oil will still be hot and thin.
Uunscrew the old oil filter with an "oil filter removal tool", then undo the oil drain plug, let drain in to a big container for about 15 mins. Refit new oil filter, but first smear some oil over the seal of the filter (helps make a good seal), screw it on hand tight.
Refill up to dipstick max mark, go for a short drive, then let sit for 10 mins, check oil again, then refil to max if required
btw on first restart do not rev it at all for a minute or so as oil has to get back round the engine and flowing throught the new filter.
Most of this is probably in the manual with pics showing where the dsrain point and filter is