Can I try it on?
'Provarlo' — the 'r' is lightly trilled. Stress 'pro-VAR-lo'.
Before taking anything to the fitting room. In Italy it's standard to ask, though most stores allow it freely.
'Posso' (can I) + infinitive is a key permission structure. 'Provarlo' = 'provare' (to try) + 'lo' (it, masculine). If the item is feminine: 'provarla'.
Posso provarla? (feminine item)
Can I try it on?
Use 'la' for feminine items like a skirt
Dove sono i camerini?
Where are the fitting rooms?
When you already know you want to try it
Potrei provarli? (plural)
Could I try them on?
When trying multiple items
Italian fitting rooms ('camerini') often have a limit on items. The assistant may count your pieces and give you a numbered tag. This is standard even in casual chains like Zara.