Buying BTC is easy today with sites like Coinbase but what was it like in 2010 and 2011?
New Liberty Exchange was up in 2009. Mt. Gox came up in mid-2010 and took up a lot of the market until its eventual collapse in 2014.
It was also more common for people to mine at home, because specialised hardware was not yet available nor required.
What wallet did people use?
Bitcoin Core. The blockchain was tiny then so it wouldn't have taken much effort (not that it really takes that much effort now).