Warning this post may be even more scattered than our typical post.
Well lets just jump right in, where to start. Do you have prime exposed soil full of organic matter just waiting for you to sow some seeds or you have a brown site where you dont want your soil to touch the ground? Lets assume somewhere in the middle, something most folks are dealing with. Medicore soil with medicore drainage and not alot of organic matter all covered in some scrubby grass.
If asthetics and time arent the greatest concerns but budget is I'd start planning a simple cheap composted no till or no dig bed. Start by either flipping all the sod or covering it with something that can smother it like cardboard or landscape fabric. Next cover it in a few inches of compost (we'll assume you either know how to produce compost or where to get it cheap) and let that settle out for a few days.
Laying logs, 2x4's, rocks etc around the edges will help contain the compost as it settles out. If the beds have shrunk a large amount during the few days of settling fill it back up to roughly 8 inches and wait. Repeat this process until you have 8 inches of settled compost and then you have organic raised beds for a small cost and not to much effort.
If drainage is an issue just build it higher stacking whatever you have around the edges, if you need to go more than a foot and have some time to wait use even cheaper materials like straw and leaves and newspaper as the base layer.