how would I use the serial ports to communicate with other serial communication devices?
Well, the answer depends on what types of devices.
Hardware-wise, if those devices are TTL-level and if you're using a 5V tolerant Teensy (3.2 or 3.5) then you would just wire each TX pin to the other side's RX pin, and of course connect the grounds. If using a 3.3V only Teensy (LC or 3.6) then you'd also want to make sure the other device isn't sending 5V signals. If the device uses RS232 levels, or some other sign type, then usually circuitry is needed to adapt to the TTL level signals.
Software-wise, if the device speaks a commonly used protocol like MIDI or NMEA0183 (GPS data) then you would normally use one of the libraries which does those protocols. But if you want to directly transmit and receive bytes, writing your own code for whatever protocol & data format your mystery device uses, then you would use Serial1, Serial2, etc as documented here:
https://www.pjrc.com/teensy/td_uart.html
If your device is actually USB, and is actually a "device" in USB lingo (has a USB B-type connector - the kind of thing you plug into a PC) then you would need Teensy 3.6, which is currently the only Teensy with USB host port capable having USB devices plugged in. There, you would use USBHost_t36 and probably
this cable.
But if you mean having Teensy be a USB serial device (where to Windows it's a COM port, or to Mac a /dev/cu... device), which is it's default and main usage mode, then you'd use the normal Arduino Serial function. Teensy-specific documentation is here:
https://www.pjrc.com/teensy/td_serial.html
I hope you can see something here, beyond the answer. When you ask this sort of very generic question, without any details and without context to understand what you're trying to actually accomplish, we have to guess what sort of answer you need. Normally I don't write out several cases like this, spending extra time to cover all the bases, only because it's impossible to get a clear idea of what type of device. But I had an extra few moments just now, and spent them on this broad answer rather than an answer that would have focused much more on whatever your situation needs.
Please, help us to help you. Try to give details and context. It saves every time and in the end we can help you much better.