If you control your own nameservers (DNS servers), then the easiest way to do it is provide an "A" record pointing to the third level domain:
thirdlevel.example.com. IN A 000.000.000.000
You will need to replace "000" with the IP of the host for your third level.
Most people do not run their own DNS servers, and instead use the servers of their web host. Based on your question, I am guessing that this is your case.
At the registrar level, the domain owner points the DNS for the second level domain, like example.com, to the name server provided by their web host. The next step is talk to your web host (or whoever is providing your DNS services), and ask them to provide a third level "A" record pointing to wherever you wish to host the third level "thirdlevel.example.com". Some hosting companies provide this service through a user interface that allows you to create additional A records, and some do not.
So the short answer is probably: "talk to whoever is hosting your second level domain, like "example.com", and ask them to provide additional "A" records. If they do not allow this, then you will need to find a new host for your domains, or at least find a new DNS service that does allow this. It is possible to purchase DNS service without web service. This allows you to leave your second level domain where it is, and just add new higher level domains.