Well I guess I will chime in here. The most important of the statements made above is use Hide glue!..For sure use hide glue.
Sinew backing or lining which it was called in the older days will even help a bow that is poorly made, I personally never sinew back a bow over 52" if you sinew back a long bow it does not help the bow as much as a shorter version, sinew works the best when it is stressed and forced to stretch, a longer bow will not put the tension on the sinew backing like a short draw bow will and usually just add weight to a longer bow rather than cast. Sinew backed bows historically were made to add cast and draw to a short powerful bow.
I use to use acetone on an osage bow before sinew backing but after over 200 (two hundred) sinew backed bows made with no degreasing and no de-lamination of the sinew I am pretty sure you can get by with out degreasing the wood.
You want to make sure your wood is seasoned, score the back of the bow very well before any sinew backing is done.
I prefer leg tendon elk for my sinew backing and will take about 6 tendons to do one layer on the bow, two layers is better. You can buy tendons cheeper than back strap sinew but they require more work, I pound them with a ballpien hammer on concrete and remove the outer sheathing, this might be greasy but the sinew will not.
separate with your fingers or needle nose plyers until the tendon is separated and will pull apart looking almost like spider webbing.
you will need to get them soaked in water and then layed out wet for a little while to soften and stretch out.
Always apply hot hide glue to the back of your bow before sinew backing, after sinew backing wrap the bow with cordage to hold the sinew in place, you can remove cordage after two or three days.
I will end for know as anybody that has sinew backed a bow knows that a whole book can be written on the subject.
good luck with your project.
Eric