If you want to migrate the data and structure from postgres table to mysql equivalent, the easiest way is using a database conversion tool like : ESF Data Migration Toolkit or the opensource counterpart openDBCopy .
If you don't want or you can't use a migration tool, and you need to only migrate data, another simple way could be export data in CSV format from PostgreSQL and then import it in MySQL, so you can do it with some commands like :
ON Postgres (Export):
COPY (SELECT query) TO '/path to csv file -*.csv';
ON Mysql (Import):
load data infile 'path to csv file-*.csv' into table tablename fields terminated by ',' lines terminated by '\n' .
If you anyway want to proceed with the dump tool(pg_dump) you can add this options to produce a dump file that MySQL can understand better :
-d --data-only --no-owner --no-acl --attribute-inserts --disable-dollar-quoting --no-tablespaces
Keep in mind that, depending on the structure of the source database, you could have to manipulate the dump file to allow MysQL to understand the generated dump file ...