How do I clean my Desktop Computer? I mean really clean it!

My desktop keeps collecting dust and then the dust just cakes on and it always seems that no amount of canned air protects the thing from grime! Now, I am not the cleanest person, but I would like to get my desktop back to some sort of “very clean” state, where the grime itself can be removed that is literally stuck to the case, external hard drives, etc. Any advice?

One last note, this was a PC I built myself, so no worries about warranties being voided or anything like that.