You can do the same, e.g. put everything in a single, broad ETF. But which is the big question.
I get the impression most in the US invest primarily in US funds. That's fine, because it's the largest developed market in the world, so lots of diversification (which you'll want always!), and most are multinationals anyway.
For us Europeans it's less simple. You are in Hungary, so you might prefer to stay local. However, I'm pretty sure the local Hungarian index does not provide sufficient diversification. You could invest Europe-wide (e.g. in the EuroStoxx 600) but that is still not sufficient from a diversification perspective.
You could go for an ETF based on a developed world equity index (e.g. MSCI World, which is 55% US) as main fund, and combine it with smaller holdings in e.g. the Hungarian index and/or other asset classes (bonds, real estate). Browse through etfdb.com or justetf.com and you'll see the options are limitless.
Hence... decide on a strategy that works for you! You can't do a lot wrong if you stick to low-cost ETFs (expense ratio below, say, 0.30%?) and go for 'buy and hold'. Don't try to time the market.