The word that describes creating, distributing, and getting the results of a survey is "conduct". So you can think of "conducting a survey" as "doing a survey". The word "conduct" is also used with a few other similar activities:
- conduct an experiment
- conduct an investigation
- conduct an interview
On the other side, the people who answer the survey questions are participating in it:
We invited about 15,000 users to participate in our survey, but only 300 of them responded.