Warframe is pretty awesome because it allows you to have a companion dog. The strange space dogs, known as the Kubrow, are of different breeds, but the very first thing you'll need to find is a Kubrow Egg. Kubrow Eggs can be incubated to generate a random Kubrow Race.
To get Kubrow Eggs you will need to head to Earth and search for Kubrow Dens. The best mission to perform is a capture mission in Mantle. This can be completed quickly, and you are looking for a Kubrow Dens on your way to the extraction. The quick mission time and small map let you run it over and over again quickly until you get the egg.
Kubrow Dens look like small, cone-shaped burrows made of wood and dirt. Each contains Kubrows that will attack you if you aggro them. You will have to attack the dens until they break apart. When they do break, a Kubrow Egg has a small chance of falling. The good news is, this is a lot more generous than it was when the feature was first added to the game, so you'll only need a few passes to get one.
When the egg drops, it will have a similar glow to a rare mod, and when you pick it up you'll get a little confirmation at the bottom left of the screen.
Now that you have your Kubrow Egg, you can head back to the Orbiter where you can incubate the egg and get your first little space pup.