Learn Italian: Lui fuma una sigaretta in giardino. - He smokes a cigarette in the garden.

In Italian, subject pronouns like lui (he) are usually dropped because the verb ending already tells us who is doing the action. Including it here adds emphasis, meaning specifically he is smoking the cigarette, perhaps in contrast to someone else doing something else.

How would we change this sentence to say 'One smokes a cigarette in the garden' using the new impersonal si?

You would drop lui and use the impersonal si before the verb, making it Si fuma una sigaretta in giardino. This changes the meaning from a specific person smoking to a general statement like 'People smoke a cigarette in the garden' or 'One smokes a cigarette in the garden.'

Why is it in giardino and not nel giardino?

For common rooms and areas around the home, like the garden (giardino), kitchen (cucina), or living room (salotto), Italian typically uses the preposition in by itself, without combining it with a word for 'the'. You would generally only say nel giardino if you were talking about a specific, described garden, like Marco's garden.