No point in reinventing the wheel so I'll post some links for your info.

Here's a "brief intro to composting: http://faq.gardenweb.com/faq/lists/soil/2000042647001285.html

That link is one of many on the one below.

All the best in your composting efforts and hope you will soon be posting to the "what have you fed your compost pile today" and the "compost wacko" threads. :-D

Here is a link that might be useful: GW FAQ about soil and compost

Forgot to say both the items you mentioned are great for making compost. However they are both considered 'greens' so you need some 'browns'. However if the horse manure has sawdust or other bedding with it that is a 'brown'. After reading all the info if you have more questions just start another thread.

I'll add that while the weeds are a great addition, the compost will decompose faster if you shred or chop them up first. I've learned that running over the pile with a mower makes this pretty easy.

Again, this is not necessary. It just makes things go faster, and depending on the weeds, might make the pile easier to turn.

There is a good tutorial on composting at the Florida's On Line Composting Center.

Here is a link that might be useful: About Composting

Yes, all of the ingredients can be used to start your first compost pile. As already noted, you'll be starting with a lot of "green" material; so, add as many ground-up leaves as you can get. You can also use hay or straw for "brown" components, and even clean sawdust can be used sparingly. Chop or shred all of the ingredients, if possible, and mix the heap daily ... or, at least every other day in the beginning. Kepp the pile moist, but not soggy. For a really interesting list of other materials that can be added see: http://compost-twin.com/ingredients.asp. Your compost is ready when it looks more like soil, and you can no longer see pieces of the original ingredients. If you plan to continuously add stuff to the pile, it's recommended that you have two piles or two bins, so that one can "cook" while you add fresh ingredients to the other. Adding some soil will also help to get the pile started, as the soil contains the microbes necessary for decomposition.