For my international stock holdings, I use a couple of ETFs that are listed on the ASX:
IVV - an ishares S&P500 index fund. very low cost
VTS - a Vangaurd total US index fund, also very low cost
VEU - an "all world but US" a global index fund, also reasonably low cost.
For domestic shares, I've used a combination of direct shares, ETF versions of index funds (VAS/STW), and LICs (closed end investment companies).
In general, I've had a bit of a focus on low cost - I think all the funds I use are between 0.06% and 0.3% MER.
I've been comfortable buying these on the stock exchange, but many offer a managed fun version (such as vanguard). I've always gone for the un-hedged versions - I want international stock to both diversify away from the Australian economy (banks and miners), and from the Australian dollar.