I just bought a new Samsung SSD 840 Series 120gb and I'm trying to get it to work and show up under my hard drives. It shows up under my bios, and I've been reading up on a guide that I may have to assign it a letter, however I see now option to do so under disk management. When I open my disk manage this is what I see..
New hard drives & SSDs are supplied without any partitions on them, consequently they are also not formatted and therefore Windows can't assign a drive letter to it and neither can you.
Without a drive letter it cannot be shown in Windows Explorer.
In Disk Management, right-click the ribbon that represents the SSD (as in your screenshot) and choose "Create New Simple Volume".
When the volume has been created, right-click it again and choose "Format".
When formatting is complete it should then have a drive letter, and you should be able to see it Windows Explorer.
It's usual to put the operating system on the SSD as it speeds up boot time considerably, and that's the primary reason why people install one. You may want to give that some consideration.