Pretty damn easy. The government even footed the shipping costs for occupation troops to send stuff home after the war, not exceeding 25 pounds, plus a premium for officers. All war bring backs were supposed to have capture papers though. Here is an example of one for a .25 pistol. It basically showed that the soldier had gotten permission to send it back, and someone had inspected the weapon to make sure it was eligible. Weapons with their capture papers these days fetch a very high premium from collectors.

Originally, you could even bring back machine guns, as long as you registered it under the National Firearms Act upon importing it to the country, but the practice it was decided that they were no longer allowed in mid-1945 (This was via Circular 155 referenced below). And regardless, in more recent conflicts, any fully automatic weapon is prohibited from import due to the Gun Control Act of 1968 (and registration was ended, period, in 1986), and I am unsure what current military policy is in general, although I know that the ATF does have a form for the importation of war trophies, so it can be done.

This document has some more information (but can't be copy/pasted so you'll have to click through). As you can see, allowing the importation of 'war trophies' was considered an issue of morale, and the Circular lays out the explicit ground rules on pages 3-7, including the prohibition of live ammo, and automatic weapons (which, again, were allowed up until then. The circular doesn't say why, but I imagine it was a headache to deal with since they had to be registered immediately upon entering the country.

Also a question: How many vets took issued weapons back home?

I think he is asking what were the rules on what can be brought back. Like could i bring back a mg-42 I found or a pistol or rifle about it?

I don't know if any Australian troops brought weapons home, is there any example of these and how did they do it. Most of these answers seem very Amero-centric