I think that sometimes we mystify test crafting when it is often much simpler and easier to do than we think. While some people will apply to be testers simply to have an early version of the pattern, the entire point of a test crafter is to help the designer before a pattern is released.
Testing a pattern for a designer is essentially agreeing to make a project based on a beta version of a pattern (kind of like being a beta reader for an author where you get to read an early version of a manuscript and offer reactions/critiques/suggestions). The ultimate goals of testing are to ensure that a pattern is clear, well-written, has no mistakes, and can be replicated by other crafters. For example, if a designer has designed a hat pattern that is supposed to fit most adult heads, then the point of testing is to make sure that other crafters will achieve roughly the same results with very little variation in terms of sizing and gauge. You want a hat that fits, not wild variations where testers end up with a hat that's either consistently too bit or too small.
Some designers and yarn vendors regularly employ or contract with testers. In these instances, the testers have been vetted, which means they most likely submitted samples of their work and have a fairly extensive portfolio and profile of completed projects to demonstrate their skills.
Most designers, though, will put out a call for testers, usually through social media, Ravelry, or a site called Yarnpond. Typically, the call will detail the requirements and duration of the test and how to apply to be a tester.
If you are very interested in testing, then I highly recommend joining Yarnpond and signing up as a tester because it's one of the easier ways to connect with designers who are looking for testers.
If you are selected as a tester, you do have several responsibilities.
You need to make sure you meet the test deadline, and if you can't you need to communicate with the designer. Meeting the final deadline for completion of a test design is crucial because designers often have a release date scheduled for their pattern, so they need the time to collate all of the suggestions, photographs, and information about the pattern well in advance of that release date. If a project seems as though it would take you longer than the deadline to complete, then you shouldn't apply to test it.
Keep in regular communication with the designer. If you run into any errors--typos, stitch counts that don't work out, instructions that aren't clear, etc., then you MUST contact the designer ASAP. Many designers will tell you that if you run into an error, then you need to STOP working on the project until they are able to correct that error. This is vital so that they know the correction works and so they can avoid any mistakes being left in the final released version of the pattern.
Follow the pattern exactly as written. This means using the yarn weight that the pattern calls for and the same needle size. You shouldn't fudge things because you, say, like sport weight more than DK if the pattern calls for a true DK, or you want to use US 10.5 instead of US 11. For some, this particularly responsibility can be difficult because they are so used to innovating and making a pattern their own. But, when you are testing, you need to do exactly what the pattern says because you're primary job is to help the designer, and if the designer calls for US 11s and DK weight yarn, then they need to know what you get as gauge when using those things.
Follow directives about social media posts, privacy, etc. Some designers want you to post social media photos related to the pattern you are testing prior to the release date in an effort at early marketing. Others will ask that you maintain secrecy until the pattern is released. Some require that you post public updates once a week and use very specific tags. Others may want you to make public posts a week or two leading up to the release of the pattern. The designer will often have a policy regarding public photos and discussion of patterns that works best for them and their marketing strategy, and it is your responsibility to respect them in this regard.
Make sure you have your own materials. Pattern design is not a lucrative endeavor for the vast majority of designers out there. Sure, some of them are very well known and designing is their day job, but most of them are designing on the side. In most instances, you will need to provide your own materials to test a pattern, and your compensation is that you will receive a free copy of the pattern itself.
Keep accurate notes regarding the amount of yarn used, the finished and blocked gauge and sizing, and the ease of the project. This information is vital to the designer and for those who will use this pattern in the future.
Testing can be a lot of fun, and there are test patterns out there for every skill level. So long as you remember that you are helping the designer and then, in turn, helping future crafters, you'll be fine.