In many cases, it appears that major news outlets (CNN, FOX, etc.) are conducting their own polls. Is this correct?
Not necessarily. As a general rule, they partner with some polling organization that performs the actual poll. For example, CNN polls often appear as CNN/ORC because they partner with the Opinion Research Council. Partnering in this case generally means that CNN would suggest the kind of questions (and possibly specific questions). The pollster would conduct the poll and prepare a report on the results. There is often a public report and a private report. The private reports often attempt to measure smaller results.
Where does this data come from?
The typical method is to randomly look for people meeting the polling criteria. This can involve computer generated phone numbers or selecting from a phone book or selecting from voter registration lists and matching to a phone registry.
The key point is that they try to minimize skew. Skew in this context means that they are polling one group at a higher rate than another group. Obvious skews would be if they had an unusually high number of Democrats or Republicans or other in the sample. They have controls to notice that. Less obvious skews could be that they had an unusually high number of hunters (more pro-gun than average) or welfare recipients (more interested in higher social spending and less worried about taxes than average).
Some links to more discussion:
Most of this discussion has started from United States examples, but this should be similar in other countries. For example in the United Kingdom, polls seem skewed against conservatives. I.e. conservatives tend to do better in elections than in polls. Polls had Brexit failing while the actual vote succeeded.
As a secondary question, how could one voluntarily participate in these polls?
Well, if they are working properly, you can't. Allowing people to self select creates skew. They'll try to call you. They won't let you call them.
You could trawl through the classifieds (e.g. Craig's List) looking for focus groups to join. These typically pay a small amount for participation (possibly in the form of gift cards). Answers are less constrained than in polls, but they also can have different results since participants can generally hear or read each other's responses. They are less worried about skew, so you might be able to volunteer for one.