Femtolisp has a nice, comprehensible Lisp reader written in C, with syntax very similar to Common Lisp:

https://github.com/JeffBezanson/femtolisp/blob/master/read.c

CMUCL has a fairly complex, but still comprehensible implementation of a Common Lisp reader:

https://gitlab.common-lisp.net/cmucl/cmucl/-/blob/master/src...

It uses a FSM to recognize numbers and symbols when tokenizing, and it demonstrates an implementation of Common Lisp readtables.

Here's how the Common Lisp Hyperspec specifies the Common Lisp reader (as an algorithm):

http://www.lispworks.com/documentation/HyperSpec/Body/02_b.h...