I have done this and have made some decent money selling finished garments.
Order Federal infantry fatigue blouse kit from Wambaugh and White. It has everything you need, fabrics, notions and instructions. You'll just need a needle and some patience.
This will show you how a version of the most commonly worn garment in the war was put together. It also clearly describes what stitches to use and where, so easily searchable online for the basics.
From there, purchase pants kit, drawers kit, tent kit, and federal shirt kit. The combination of those five garments will give you practice in basically every method you'll need to know, and give you a wide range of examples on how common garments were constructed.
I would recommend against trying to draft a pattern like others are suggesting unless you are copying from an original you have access to. Most garments that federals were issued came from fairly widespread or at least regional patterns. We know these exist and we know where to find them. So why not use patterns off original garments rather than fashioning something you think will fit and ends up looking like a vintage (nineteen) 60s pajama top?