Pretty straight forward.
The ongoing for the funds are 0.22%, the ISA platform 0.25% and the SIPP 0.3%
[0]http://www.morningstar.co.uk/uk/funds/snapshot/snapshot.aspx...
[1]http://www.morningstar.co.uk/uk/funds/snapshot/snapshot.aspx...
So just log into your account, find the ticker, and buy it.
Some individuals (such as yourself) are not eligible to receive a SSN. For those individuals who need an identification number for US tax purposes, the IRS issues ITINs. See here for more information: https://www.irs.gov/individuals/individual-taxpayer-identifi...
If you want to invest in a US index, you can probably find a ETF traded in your country of residence that tracks a US index. It'd cost a bit more than Vanguard's, but would cost you much less in hassle, effort, and regulatory requirements (which would be handled by whoever manages the fund).
You should ask your broker or bank about that before rushing to try and buy Vanguard's ETF directly from the US.
I'm a French citizen, and wish I could help you regarding investing in the EU, but unfortunately I only got interested in it after moving to the US. Back in France it seemed like most people invested in real estate rather than in the markets.