You can devise a jig of some kind to help in making multiple pieces of smaller size but at heart producing strips of wood like this doesn't have to be any different from getting a board to final dimensions for the face of a drawer, a shelf, the side of a bookshelf etc. etc.
The thinner dimension does mean you have to be more careful in sizing as there's a smaller margin of error allowable, but the basic principles remain the same.
For pieces of small cross-section often you'll saw roughly to size from a larger board, i.e. resawing or ripping lengths from it, after that the same process you'd use to make a shelf to the size you want comes into play.
You start with one face of each piece (usually you pick the one that's flattest already, sometimes the side with the best grain) which becomes your first reference or datum surface — the face side. After it is flattened and smoothed then you plane an adjacent edge — the face edge — dead square to the face side. Once these are established (and marked so you don't lose track of them) you can gauge lines for width and thickness from them, then you plane to final dimensions. Working from surfaces you know to be straight and square helps in producing a finished board that's straight and square.
This is a fundamental of hand-tool woodworking, laid out in any good book on the basics for learner woodworkers, e.g. Robert Wearing's The Essential Woodworker which many good city libraries will have a copy of. Online, there's a very detailed show and tell of the entire process starting from rough-sawn wood available on Wood and Shop's site, How to Square, Flatten, and Dimension Rough Boards with Hand Tools.
If you had to produce a great number of lengths of wood to exacting standards it does become a process that perhaps is best jigged, for speed as well as to help with consistency, and actually Robert Wearing would be a fan of that sort of thing. I think he covers something applicable in one or more of his other books on jigs and workshop aids.