zone 10? I assume that's in my settings? I'll have to try and change that.

I don't want to use my soil as it's too difficult to dig up, with it being a solid clay, so I am going to go down the raised bed route anyhow.

If I use the raised bed, I would need to add topsoil I think, as well as manure. But how much soil and rotted manure should I use? Should I use 50% topsoil and 50% manure? Or should it be mostly topsoil but with a thick mulch of manure?

Why do you need Alfalfa Hay?
What dou you think "topsoil" is?
Alfalfa does have some Nitrogen whihc can be obtained from amny other sources, compost for example. Manures could be used, but keep in mind that manures are carriers of several disease pathogens. "Topsoil" is also not a magic elixar and most often is not anything worth what it cost.
Raise beds may need soil and some organic matter, and like ground level gardens the amount of organic matter in any raised bed is around 6 to 8 percent.

Organic - unless you live in a newly built house where the builders have removed the topsoil you already have 'topsoil' in your garden. It may be clay soil but it is probably absolutely fine as the basis for starting to garden. I have very heavy clay but with compost and muck added it grows good crops. There are not many places in Southern England that do not have soil which will make a reasonable garden.

If you really want to be planting stuff out in a couple of weeks you are looking at a large outlay in bagged compost and loam to fill raised beds that fast. I really do believe the cheaper, and in the long run, better option would be to dig the ground you have. It's more work but will give you a good garden. However, if you are set on filling up raised beds about 2/3 potting compost to 1/3 garden soil or John Innes would be about right. Plus you will need some sort of retaining edging unless you are just going to mound the earth up. This is going to be very expensive.

It would be highly unlikely that anyone would find bags of Loam being sold in stores, something called "garden soil" or labeled "topsoil" but Loam, being a specific soil type and not very common can be difficult to find.

In the UK there is a British Standard for topsoil and it is based on loam, being a mix of sand, clay, silt, and organic matter. There is also readily available John Innes recipe compost which is also loam based.
http://www.jima.co.uk/about.htm#WHAT ARE THE INGREDIENTS?

So the OP should be able to find loam-based composts pretty easily, though at a price.

Here is a link that might be useful: Topsoil

You might consider straw bales. They can form their own raised bed in 2 different ways, one as the outside frame of the raised bed to be filled with compost or second as the raised bed themselves. I'm trying them as the raised bed for my first time this year. They say to season them with ammonia sulfate and compost, then you can plant right in them. in 2 years they will be composted and you can work them into your clay soil, and/or just stack new bales on top and repeat the process.

Hi flora uk, I think it is great that there is a British Standard for topsoil. If there is one for the USA, many do not use it. I have some bottom land(swamp) that is BLACK & Loamy with organic matter. A man with a dump truck tried to buy the top 12"(30cm) from me. I later found out that he & others would mix it: 1 part soil & 2 parts sand, to sale as top soil.
People here think black means rich when it is soil. The truth is that it means high water level, which is in a bottom or low place. The silt some times carry micro nutrients, but this is the best case & the persons selling it(in the USA) do not care what is in it.

jolj, since sand is a component of soil explain what you mean by, "1 part soil & 2 parts sand".
While there are several different types of Loam, generally it consists of 45 percent sand, 25 percent, silt, 25 percent clay, and about 5 percent organic matter. You cna have clay loam, sandy loam, etc. which changes the proportions some, but loam is not a very common soil type found every where.
There are no rules and regulations that require people selling soil to adhere to, and in the market place in the USA "topsoil" can be what ever the seller wants it to be.

I came here to the UK from Australia 5 years ago. I used no-dig gardens extensively there - the main reason being that the soil was clayey and hard work to dig, and I'm not really physically up to doing a lot of that, plus, a raised bed is much easier for me because I don't have to bend down so much. I definitely wanted to do it here as well, but the lack of lucerne hay for gardening surprised me. We ended up following the same formula that I used in Australia - except that we used straw instead of the lucerne hay http://www.abc.net.au/gardening/stories/s867068.htm It works okay but I don't think it has quite the same benefits of extra nitrogen, and there are also bits to be weeded out from sprouting seeds at first. Our no-dig gardens are contained in boxes that my husband builds from wood planks from the hardware store (no base of course). We are investigating whether we could get pea-straw as it would be good for nitrogen too.