What does "not detected" really mean? Remember, we can't see your screen. We don't know what you're actually seeing.
If you're looking at the Tools > Ports menu, using version 1.41 or earlier, it's perfectly normal for the board to not appear in the menu at times. Teensy by default uses HID protocol, not serial. Starting with 1.42, which is still in
beta testing, the ports has been redesigned to show all possible modes. You might prefer to install the beta for the better ports menu...
When you click Verify or Upload, you should see the small Teensy Loader window appear after Arduino finishes compiling your program. If you don't get that window, check Tools > Boards to select the Teensy board you have.
That small Teensy Loader window is the best way to troubleshoot. Its toolbar has 4 buttons, where the one on the first right is "Auto" mode. A successful Verify will turn that on. For troubleshooting, click to turn off Auto mode, so Teensy Loader doesn't quickly program your board the moment it appears in bootloader mode. Normally you want it programmed right away, but for testing you want Teensy Loader to keep showing you a visual confirmation that doesn't disappear rapidly.
While your Teensy is blinking, press the button on the board. 2 things should happen:
#1: The blinking should stop with the LED off, which is a good confirmation the hardware is working. If it keeps blinking, that's a sure sign of a hardware problem like a broken button.
#2: The Teensy Loader window should change from "Press Button on Teensy to manually enter Program Mode" to a bright picture of your Teensy board. If you don't get any response in Teensy Loader, it means your computer isn't able to communicate with the board. Charge-only cables (missing the data wires) are the most common problem. On Linux (we don't even know which OS you're using) forgetting to install the udev rule file means non-root programs can't get access to the hardware. Other problems like damaged USB connectors, bad hubs or ports, or horribly messed up drivers are much less common, but still could explain why it can't communicate.