Ensure you have a Raspberry Pi installed with Raspbmc and connected to your home network. See this post for how to do this.
Note down the IP address of your Raspbmc. (For example: 192.168.0.12) Follow step 1 of this post to find the IP address of your Raspbmc.
From the computer you want to FTP, ensure that you can ping the Raspbmc. For example: ping 192.168.0.12. If the Raspbmc is not reachable, check the settings of your wireless router or home network.
Open a FTP program and connect to the IP address of your Raspbmc using Secure FTP (SFTP).
Login using the default username (pi) and password (raspberry) of Raspbmc. For example, I open Filezilla → Site manager. In Host enter the Raspbmc IP address, choose Server Type as SFTP, Logon Type as Normal, enter the username and password and click Connect.
Transfer the files you want between your computer and your Raspbmc. For example, if you have a USB thumbdrive or harddisk plugged and mounted in your Raspbmc, you could transfer files to the drive directly from your computer using FTP.
You may need root access to transfer to certain directories and mounted drives. The root account is disabled by default on Raspbmc. To enable it, SSH into your Raspbmc (see this post on how) and follow the directions here to get root access. FTP into your Raspbmc using root account and you can do these file transfers.
Tried with: Raspbmc 12.0-ALPHA5