Each console can have up to two devices registered to it and connected at once for a maximum capacity of 32GB. To use a USB flash drive, you must first configure it in the memory area of the 360's system settings menu, committing up to 16GB of space to console use exclusively. You can also hook up an external hard disk drive, of course, but no matter how large the drive is only a 16GB partition can be made.
To support the new functionality, Microsoft has partnered with SanDisk to sell pre-configured, 360-branded 8 and 16GB flash drives for release in May. Both are available for pre-order now priced at $35 and $70, respectively -- which, unsurprisingly, is quite expensive considering you can get the same amount of storage elsewhere for $15-30.