While you can paint warps while on the loom, that sounds too messy for me.
This is a method that I learned while taking a workshop with Eileen Hett and Mary Berg.
The way I painted my tencel warp using Procion MX dyes was as follows:
Wind warp. Tie cross firmly, but try and use a different type of fibre from your warp yarn (eg use protein fibre if warp is cellulose fibre). My warp was short so I didn’t use any choke ties. For a longer warp I would have made figure 8 ties about every 2 yards or so to prevent major tangling.
Weigh your warp while dry and record weight (needed for dye process).
Soak your warp in water and with appropriate amount of fixative (either soda ash for cellulose fibres like tencel and cotton, or vinegar for protein fibres like silk or wool) for about 30-60 minutes (I got figures for amount of water and fixative from “Hands On Dyeing” book)
Cover surface (floor, large table, etc) with wax paper or something to protect it. Then cover that with plastic wrap the length of your warp.
Remove warp from water/fixative solution and squeeze out excess water. Lie warp on prepared surface, spreading warp as much as possible. Remove ties if you have used them.
Paint your liquid dye solutions on using paint brush, sponge, syringes, whatever you can think of. Make sure dye gets through to back/bottom yarns in warp, and doesn’t pool underneath warp.
Once you are done, roll the warp in the plastic wrap and leave 24 hours, then rinse and leave to dry. This is how I did mine….. others might have different methods. Also if you use weak acid dyes, you need to steam or heat warp to set it after painting.
Hope this helps (and that I haven’t left anything out!) If you have questions, please ask and I will try and help. This was a relatively new experience for me too, and lots of fun!
Books – Dyes and Colour
Color by Accident: Low-Water Immersion Dyeing
The Yarn Lover’s Guide to Hand Dyeing: Beautiful Color and Simple Knits
Yarns to Dye For
Hand Dyeing Yarn and Fleece: Custom-Color Your Favorite Fibers with Dip-Dyeing, Hand-Painting, Tie-Dyeing, and Other Creative Techniques
Yarn Works: How to Spin, Dye, and Knit Your Own Yarn
Tie-Dye: Dye It, Wear It, Share It
Prepared to Dye: Dyeing Techniques for Fiber Artists