First, check your wiring. Make sure you've got power, ground, and data all connected to the right pins on your microcontroller and that you've soldered to the IN pin and not the OUT pin.
Next, check your code. Does your code specify the same data pin your strip is connected to? Make sure they match -- if you soldered to A1, be sure you've called A1 in your code.
If you're using code you found on the internet or wrote yourself, put it aside and upload some tried-and-true sample code. There are code samples on the guide pages associated with all the microcontrollers Adafruit sells. Using strandtest or example code will eliminate some variables so you can confidently test your physical connections.
Then check your power. Are you powering from a battery? Check to be sure it's got a charge, and if there's a switch on your battery case, make sure it's switched on. Try plugging into USB to see if that fixes the problem. If it does, make sure your wiring is correct -- on some microcontrollers, connect your red wire to BATT for a battery powered project or USB for a USB powered project.
If you're using a Gemma M0, there's a tiny on/off switch on the face of the board. Make sure it's in the on position.
Here are a few more common problems, and their solutions.
Data Wire Connected to OUT instead of IN
This is one of the most common mistakes, and even seasoned veterans still do this on occasion. If your strip isn't lighting up, double check that you've soldered to the IN end.
Loose / Unconnected Ground Wire
If your ground wire (GND) has a bad connection, the strip will often flicker like in the image below. Check all your ground wires and make sure you've got good ground connection on both ends of the wire. This can sometimes happen further down the line in larger projects with longer runs of lights, so another thing to try is to connect a second ground wire from the far end of the strip back to the microcontroller.
Bridged Solder Pads
This strip has too much solder on the GND pin, and it's muscled its way over onto the DIN pin. You can fix it with a little solder wick - just remove some of the extra solder so the two pads are not bridged.
If your ground wire and your power wire touch each other at any point, you'll get what's called a short circuit. Your microcontroller will reset and your strip will go dark. If this is happening to you, check to be sure there's nowhere that ground and power can touch.
This happens pretty commonly with alligator clips, if you're moving your project around while it's turned on. It's not great for the microcontroller so try to avoid it -- if your project uses alligator clips, cut the lead wires to uneven lengths so the alligator clip heads aren't all right next to each other.
Only Half the Strip Is On
If the first half of your strip is working fine, but the second half is off, the first thing to check is your code. You have to specify how many LEDs are in your strip in the code, and if you downloaded sample code without editing it, or ended up with more LEDs than you thought, this could likely be the problem. Check your code before you cut into your strip!
If that's not the problem, you have a bad pixel or a damaged strip. Sometimes the copper pads can get torn if the strip is flexed too much. Take a look at the Tips & Tricks page for a couple ways to fix this.
If none of this helps, drop us a line in the Adafruit Forum. We've got customer service reps who are very excited about helping you with your project.