When scheduling a "class", the only trainers that will display are trainers approved to train the "course" which is set-up course manager side of the system as you might schedule a class for the course an number of times. Simply go to Course Manager, look up and select the course, click the Trainer Tab and add your trainer. Once a trainer is added, they are eligible to be a trainer for any scheduled class. 

IMPORTANT: When adding trainers to a course, for the trainers to appear in Master Schedule when scheduling a class, at least one trainer must be designated as primary trainer. 

(For some clients we have built a housekeeping function that auto-adds trainers to the course (and removes them) based on having completed prerequisite training, some attribute on the learner record or processing some external file. There is a small professional service to set this up, but it can save you a lot of time. )

If a trainer is not assigned to the course, from the trainer tab in a selected class in master schedule, click the + icon. This window also defaults to only trainers assigned to the course as previously described; however, there is a check box at the bottom of the form to select all trainers, and this will list all trainers in the system as shown below: