How do I cook chicken and asparagus over an open fire?
You have two delicious choices. Both require a bed of coals, so I'll start with that.

You'll need to build a fire with the logs stacked 'log cabin' style, and let the fire burn down to coals. You want a deep red coal, just starting to darken on top. The coals should look something like this.



You can bake, or bbq the chicken and asparagus. Both are delicious methods.

To bake, wrap the chicken, asparagus and a starch like potato gratin style in layers of tinfoil. Use the starch around the outside, you'll sacrifice a layer of it as some of it sticks/burns to the tinfoil. Put the most delicate item in the middle, in this case the asparagus, and the chicken around the asparagus. Add a generous amount of butter, salt and pepper and bake for about an hour buried in the coals. Corn or green beans are also very good, and can be sacrificed a little around the outside to preserve your meat and vegetables.

I would layer it this way. 

 1.Coals
 2. Tinfoil
     2. Potatoes 
     2. Generous dollop of butter
     3. Salt &amp; Pepper 
     4. Green Beans 
     5. Asparagus
     6. Chicken 
     7. Potatoes
 3. Tinfoil
 4. Coals


Now, BBQ. You'll do it very much like a charcoal BBQ. Keep the grate close to the coals, you can generally test the heat by holding your hand above the grate, you should only be able to keep your hand there for a second or two at most. 

Grill the chicken like you would on a bbq, and roast the asparagus on a cooler part of the grill. I'd marinate both before putting them on the grill. I'd also try to get an aromatic wood like hickory or mesquite, pine will impart a resinous taste.