Examples are good, so here's a account of how we did it, which I believe is the standard way. I've changed the numbers to make it easier to understand.
When I and my two co-founders started, we each bought 10 shares in our freshly-incorporated company, paying £1 for each share. At that point we had what was effectively a shell company with just £30 in the bank, with 30 shares issued.
We then went to our investors -- we'd spoken to them before, and had agreed on prices and equity splits so on -- but at this point we all formally agreed that we all thought that the company -- with its £30 in assets, but, more importantly, the founders working for it and our business plan behind it -- was worth significantly more than its £30 assets in the bank. So they agreed to pay £10,000 for 33% of the company. This meant that we (the founders) issued another 15 shares, and sold them to the investors for the £10,000 they offered.
Once that was done, the company had 45 shares issued; the investors had 15 of them (thus, 33%) and we each had 10. Of course, that meant that we, the founders, had been diluted (my 10 shares were originally 33% of the issued ones, but now they were 10/45 = 22%) but that's what happens when you take on investment.
It also meant that the investors paid 10000/15 = just less than £666.66 per share, while I and my co-founders paid £1 per share. But these investments happened in different rounds, so that's fine. At the end of the day the price of a share is whatever buyer and sell agree on. When I bought my shares, I was just putting money into an "empty" corporate vehicle. When the investors put in their money, they were putting money into a company with a business plan, founders, and so on. So I bought into something worth very little, and they bought into something that was (we all hoped!) worth a lot more.
Hope that helps.
