First, if your hair has suddenly gotten dry over the last year, I would have a reputable hair dresser check it out. It may be that your hair is severely damaged and your regular haircuts are not removing all of the damage. I used to get my hair cut only once a year (long hair) and my hair dresser very bluntly told me that either I would need to come in more often, or I would have to let her cut more hair off because the amount I was telling her to trim wasn't enough to remove the damage. Once hair is damaged it can't be fixed and needs to be cut. (Commercial hair products lie telling you the product can fix damaged hair. It can't. It won't.)
Ok... that said... you're going to find a lot of ingredients, a lot of variables once you go down the rabbit hole that is making your own hair care. Typically a good shampoo bar will use at least two surfactants, typically SCI or SCS, with coco b* and SLSa. *sorry I shortened this because I can't ever spell or pronounce it right. Google CAPB and you'll find it.* A conditioning "wax" such as BTMS-25 or BTMS-50, some may use cetyl alcohol depending on the BTMS used. Optional ingredients may include oils, butters, panthenol, various proteins, silicones and sodium lactate or stearic acid. It's not anywhere as simple as soap, there's no shampoo bar calculator, and you have to take pH into consideration, as well as the molecule charge (cationic/anionic etc) - dear lord, I hope I said that right. I confess that last part still confuses me and I'm still working my way around understanding it.