If you are out shopping in Italy, and you can't see what you want to buy, the easiest way to ask for something is Vorrei comprare ... (I'd like to buy ...) followed by the name of the item.
One you have decided that you are going to make the purchase, you can smile, nod and say grazie or perhaps try Va bene, lo compro. Mi piace molto 'OK. I'll buy it. I like it a lot'.
Buying things. General phrases. 2.
If you have a (slightly) more advanced level of Italian, this has more advanced shopping phrases with Italian transcriptions. So you can pick up expressions such as Che taglia indossa 'What size are you?'.
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