Hi, I'll get my Teensy 3.6 today and the only component I have to play with it is an I2C 5V LCD module...
Being a total newbie, I wonder if any arm can happen if I just try to use the LCD module with the 3.3v out of the Teensy (and I2C wires of course), without any pullup resistors, except that the LCD could not operate at 3.3v (being to dark to be read for example)
As Frank B says, the 3.6 is not tolerant of 5v at all, and you are likely to fry the 3.6 if you use a 5v connection.
To do it properly, you need a bi-directional i2c level converter that you plug 3.3v, SCL, & SDA on the Teensy to one side, and 5v, SCL, & SDA on the remote side. Some provide a ground pin to connect as well. If not, you need to connect the grounds between the Teensy and the display. If you are powering your Teensy via USB, you can use the VIN pin on the Teensy to provide 5v power to the display. Here is the i2c level converter that I've used in the past:
Note, many displays will work with either 3.3v or 5v. Some of the early i2c displays that I got were 5v only, but most things you buy today are dual voltage.
If you had a 3.3v capable display and didn't need the level conversion, you may need two pull-up resistors (in the 2.2k to 4.7k range). One resistor would connect to the Teensy's SDA pin and 3.3v, while the other would connect the SCL pin and 3.3v. You might not need it, if the display has its own pull-up resistors (some do, some don't). On an Arduino AVR system like the Uno, you don't need pull-up resistors, since the chip has strong enough internal pull-up resistors. On ARM based systems like the Teensy LC or 3.x systems, you tend to need the external pull-up resistors.
If you just want status messages, you can use the serial monitor on the IDE session, using
Serial.print and
Serial.println statements. These is a button in the upper right of the Arduino display to bring up the serial monitor.
The way to see if you need pull-up resistors is to bring up the example Wire -> Scanner. Start the serial monitor, and download the scanner example to the Teensy. Every 5 seconds you should see a line saying Device such and such. If the scanner example hangs, that is a sign you need pull-up resistors. If the scanner example loops printing, but does not print a device, that is a symptom that something isn't connected correctly.
Rather than fritz around level shifting, it might be simpler to get a new display. PJRC.com offers a TFT LCD display (320x240 pins) complete with touchscreen for $15. Note, this is a SPI display rather than I2C, so the connections are a little different:
You can get cheap 128x64 OLED displays on ebay. These may or may not have pull-up resistors. For example, from US sellers:
I believe the Adafruit displays do have pull-up reisstors already in place: