Both you and the recipient would need a bitcoin wallet address. There are many options for wallets. Some live on the web, where others can be stored on your hard drive or thumb drive.
To send bitcoin, you would need to connect your wallet to the web. Each wallet should have a “send” option, and you just enter the bitcoin wallet address of the person you want to send to.
The public portion of the wallet address are recorded in the transaction, which is also public. The actual names and identities are not recorded, just the public portion of the wallet addresses, and the amount of the transaction.
There’s a lot of faith in unseen things required in trading bitcoins. I’ve been mining/trading cryptocurrencies for several months, and it still looks like voodoo to me.
No warm-n-fuzzies if you've been doing it and it's still voodoo.
Now, there must be thousands or more folks (well, their PCs are doing the mining) mining bitcoin at any one time. Is this totally distributed? If so, whats to prevent someone "spending" tons of resources in time, money, CPU cycles, etc, perhaps only an hour away from finding a new unit of bitcoin from being superseded by someone else doing the same, only a bit quicker to the draw?
If all bitcoin mining at anytime is centralized, sounds like a lot of network traffic occurs while doing so.