To the point, most people don't actually understand how design might help them and their business. People think designers are out there to just to make things look pretty, don't add much value and should do it for free because it's what they love to do. The same also applies to photographers.
I've noticed that you either understand design or you don't. Some people get it while some people think it doesn't matter at all. If it were that way we would all be driving the same cars, would all have the same computers, the same clothes and so on. Many don't look at the broader picture. Most successful companies in the world are successful because of their designs, companies such as Ferrari, Apple and Ralph Lauren - these companies aren't popular because they just make stuff, they put thought into the design of their products.
Be upfront and tell clients why you're worth however much
Some clients are usually after the cheapest possible option rather than looking for high quality and long-term value. You need to tell and show clients why you're worth how much you're charging and the benefits they will get from hiring you.
Some clients also think they're creative enough to know exactly what design they want and think it looks great - unfortunately they don't see how deluded they are, and as much as you try to explain why that design is ugly, they still think they know what they're doing. When you're put into this situation stand your ground and straight up say no, you won't do it, even if it means you'll lose the client. Why do you want to pollute your portfolio with work which is no where near the quality you know you can produce.
Design is objective
There is no "right" design. Everything is based on preference so some clients will find it hard to value your designs.
Because I like my minimalism, people often question how much work I put into designing something. Many will think "surely it can't be that hard" so they think I'm not worth the money. Other designers will understand how it isn't easy to just whip up a design and be happy with it. It can take hours, even days to come up with a design which you're finally happy with. When you're a designer you take into account all the little things which others won't particularly notice.
In a situation like this if the client thinks that it was an easy job and they could do it themselves, explain how hard it is, explain how you had to find inspiration, had to make notes, had to try variations and whatever else.
Don't undervalue yourself!
I find it amazing how many designers these days hugely undervalue themselves. These designers could easily charge £40 an hour or more but they choose to charge only around £10 an hour. This causes problems for high charging designers who charge a lot more - because some clients don't see the value from the high charging designer and think the cheaper option will be better.
The more you charge for your work the more seriously a client will take you. It'll also push out the clients which are looking for something cheap. So the clients you get will only be serious ones, who will usually know what they want and are willing to put a lot of money on the line for it.
This will not only enable you to gain a very nice income but because you're charging a lot more you'll want to put the work in, you'll want to do your best every time - it's a great motivator to become better at what you do.
Have the confidence to say no to a client
Some clients aren't very friendly, they think because they're paying you, you're essentially their slave and should do what they say. From the beginning you need to be confident, you need to show that you won't take any sh*t from them - this doesn't mean you need to tell them this, it's all about the way you come across, how you talk and your knowledge.
If a client comes up with an idea or design which you know won't work simply say no. Don't just go with it. Once your advice pays off they'll then see your value not just as a designer but an advisor and consultant too. They'll notice that you actually want to help their business succeed and are not just looking for cash.
Of course all the above only applies to some clients. Usually most clients are very nice and know what they want but will always take on your advice. They'll understand that you're a freelancer and not their employee.
However when you're a freelancer you really need to stand your ground and show your worth. If a client doesn't see your worth then you need to stay away from them even if it means you'll lose out on some cash. You need to know what you're talking about, you need to be confident in your work, you need to be able to tell a client their idea is crap and you need to add value to your work.