One of the fastest ways to acquire Gridcoins, is investing and trading. You can trade other cryptocurrencies for GRC over at specific exchanges. I will list these down below, as other most important sites for trading and investing.
However, if you want to invest money into GRC, at the moment you need to first buy other cryptocurrencies, which you then trade for GRC. This can be done on multiple sites. (This can and most likely will change in the future)