When you talked about mining bitcoins, that happens when your wallet solves enough mathematical problems to verify enough of a block/s that you can be awarded some bitcoins. This is typically not cost-effective, at least for most normal computers, as generating them is fairly slow and energy-intensive.
While the warnings are valid (that mining may not be cost effective for most computers), this is not a very good explanation of the mining process. I suggest you search the forum a bit if you want to understand mining better.
The only alternative to get substantial amounts of bitcoins, buy buying them, can only happen if you find someone who wants to sell you bitcoins.
Actually there are other alternatives:
You can provide a product or service and receive bitcoins as payment.
You can exchange your local currency for bitcoins.
You can beg and hope people will donate bitcoins to you out of the kindness of their heart.
(I suppose you could also consider scamming/stealing them)
The most reliable way is through the sites you mentioned, however if you can find some user out there who is willing to trade, say via an irc channel, or some other way, you are free to trade that way.
Some currency exchange suggestions are:
- MtGox.com
- coinbase.com
bitfloor.com- localbitcoins.com
- IRC bitcoin-otc channel
- bitcointalk.org currency exchange sub-forum
This is less safe though, which is why it is better to stick to the trusted exchanges and marketplaces.
Less safe how? Explain? I haven't found anything less safe about it than using an online exchange.
EDIT: As of 2013-04-17 BitFloor has ceased all operations.