Here's an example of the variables in such a project with regards to skill, design, and budget:
My eight year old son wants a desk for his room, I really want to make one, but after looking at all the furniture on this site, I am not capable and would not even know how to begin. Are you planning on building something that is 'heirloom' quality or something you won't mind handing down to another youngster when he outgrows it?
What does the plan entail? Drawers? Shelves? Roll top? Laminate?
I have a limited number of tools and have no idea how I would make boards wide enough for a desk,
Bar/pipe clamps or a bench top/sheet of plywood with with cleats & wedges to hold boards tight together could be used here. plywood itself makes a good desk top if you edge band it with iron on banding or hardwood strips.
I assume I need a jointer to work the edges
You could also use a router table or stationary base with a good straightedge and a good 1/2"+ diameter x 1" long straight bit.
and maybe a biscuit cutter or dowels to assemble my wide stuff
Not necessary unless you think so. Many panels are glued up without biskits or dowels.
but then wouldn't I need a planer?
Are you starting with dressed lumber? If so, you could use a hand plane and card scraper to get the surface even & smooth. No sanding may be required this way. With rough lumber a good bench plane and a lot of elbow grease is required. Don't forget you need to know how to sharpen all these hand tools.
Then how would I cut the joints for assembly?
Would I rabbit, dove tail, not even sure how to make any of these, do they require special tools? Miters? (miter saw, hand saw/plane if you're good, table saw, radial arm saw, circular saw & square). Dadoes (router, table or radial arm saw & dado set, hand saw & chisel), dovetail (back saw or coping saw& chisel, router & dovetail guide w/bit)
I guess I would need a router or router table to make the edges look nice, etc.
Not necessarily. Edges can be made to look nice with a hand plane by easing the edges. Or, you can invest in an antique molding plane and dress them down that way.
I guess it is like a recipe, if I have all the ingredients, I can make the dish. If the desk plans list all the tools needed, I would know if I can even start the project.
It IS like a recipe, but one in which you need to know that sometimes substitutions can be made without compromising the finished product. And you haven't even started to talk about finishes yet.
What I guess I'm trying to say is don't be afraid to get your feet wet but don't jump off the deep end of the pool before you know how to swim. Build your skills on basic projects using inexpensive materials first to achieve a skill level where you feel comfortable with advancing. No one here started out knowing how to do this. Take an objective view of your projects & learn from your mistakes (you'll make them). You could take any project on this site and follow the instructions given and not get good results if you haven't achieved the skills levels required to execute the tasks described.
What tools do you have now? I'm sure there are enough WWers here to give you ideas on many projects you could do with the items in your tool box if they are in reasonably good condition.