2 modules: api and service. api depends on (requires) service.

Compile the service class and module (has to be compiled as well). Output to service/target/classes.

javac \
    -d service/target/classes \
    service/src/module-info.java \
    service/src/example/service/Service.java

Compile the API class and module. Output to service/target/classes. Pass a path to the service module that api depends on.

javac \
    -d api/target/classes \
    api/src/module-info.java \
    api/src/example/api/API.java \
    --module-path service/target/classes/

Run the api module with main class example.api.API specified. Pass all required classes and modules in the module-path (colon-separated).

java \
    --module-path service/target/classes/:api/target/classes/ \
    --module api/example.api.API