You will re-spawn as the Shrimp if you did not reach Pig or Crab before dying, and you spawn in the ocean.
The Shrimp is one of the simplest and smallest animals in the game - only freshly-upgraded Rabbits and/or Trouts and/or Arctic Hares are slightly smaller. It is one of three animals without a tail, the other two being the mouse and the Chipmunk. Its base color is orange and features several embellishments, including its image-only tail, and slightly darker orange stripes.
The first thing you'll want to do is to find a Plankton bush, as this will be your quickest method of getting to rabbit or trout. If you can find a plankton bush, your time as shrimp will only be a few seconds at most. As an added benefit, finding a plankton bush that has a Hiding Hole in its proximity will allow quick escapes from swarming predators.
Always be on the watch for Trout, Crabs, and even Squid hiding in a berry bush you might want. Be wary when getting close to a hiding hole, as smart predators might be lying in wait, though this goes for all animals and not just Shrimp.
Fortunately you won't have to worry about predators beyond Trout and the occasional Rabbit, since most larger predators consider it a waste of time to chase after Shrimp, since they give relatively little XP compared to bigger animals. Still, this does not mean you should run up and bite a Squid's tail!
There's also a way that'll let you level up fast and give you a good start boost. You have to stay as a Shrimp and look for a big animal outlined with red that'll most likely not care about eating you (Squid, etc...) and then bite his tail, if he tries to eat you then run, if he doesn't, continue biting! This can be better explained in the video provided below.