There are a few times when you know it is time to seek a coach.
You want to learn something very technical, like Olympic lifts
Olympic lifts are highly technical and need a good degree of practice in order to be done safely. A quality coach can help you find your grip width, look at areas that need better mobility, and see where your strengths and weaknesses are.
You want to compete
Competition is great to have, and you do not need a coach just to compete. However, to win, you will have a much better shot if you have a quality coach at your side writing your workouts and helping with things along the way.
You are coming back from injury
Injuries happen to everyone, and sometimes they happen because of negligence, or other times because of overuse. Either way, it is important to find out if the injury occurred because of overuse, or incorrect form. It is beneficial to seek someone with an eye for form in order to avoid any future injuries.
A coach is able to take your performance to the next level. There are levels to everything, but they are even more clear in the fitness world. For example, the average gym goer may have decent form that any qualified personal trainer could help improve. However, the average personal trainer is not able to take someone to the Crossfit Games or the Olympics, that requires a much more experienced coach.
A coach is also able to speed up the learning process by a significant amount. Anyone can learn anything that they put their mind to, but a coach will ramp up the speed of it. Plenty of information can be found on the internet, and it will allow for gradual improvement. In that case it is almost strictly trial and error, which works over time. A coach with a great eye is able to correct form, posture, and movement in real time. They can critique grip width, stance width, and overall movement quality in person. This is a massive bonus because they know what they are looking at.
Generally a quick google search is able to give you all you need to find a quality coach in your area. Always try to find the best coach possible, even if you have to drive a bit in order to see them. Another way is to find coaches that are certified in the sport that you want to improve in. For example, if you want to compete in Olympic lifting, searching for USA Weightlifting (USAW) coaches in your area is a good place to start.
The next step is to look at the track record of the coaches. If they have not produced a quality athlete before, then chances are that they are either inexperienced or not worth the investment. Finding a coach whose name carries a bit of weight is what to look for. A well respected coach that has produced results many times before will be able to take you wherever you want to go.
Coaches are useful in every aspect of life, whether it be fitness, business, or mental health, they are resources to take you to the next level. An investment in a quality coach only pays off over time.