"The drivers that I require should actually be on the Windows 7 installation media"
Correct.
"is there a secondary way to get them, downloading them from Microsoft or Dell perhaps"
No. I am not aware of any way to obtain them except from the Windows media.
"At this point I simply install it from the disc, but then I use the disc to boot, and search for the drivers that way? This is where I'm getting mixed up"
Yes, you install from the Windows 7 disk, and once installed, then install the drivers for whatever devices need them. It is just like an OS install on a regular computer. If you haven't installed an OS on a PC before, then this may be a bit of a chore and a bit daunting.
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I'm assuming there is no attempt here at "upgrading" ... there is no upgrade path whatsoever between server and client OS's. Since it is not possible, yes, a clean install is in order.
Don't count on SBUU/SMTD working to install Windows 7 - it does not support client OS's. Install directly from the OS media.