Never alarm end users by telling them that their problem is too difficult to solve or that it has no solution. If that time ever comes, always remember to be professional and let the client know that the problem will be resolved, but you might need to transfer it to a different technician. By doing this, the customer will recognize that you truly care and that you have their best interest in mind. Furthermore, make sure that there are no distractions around when you are providing remote support assistance to a client, such as a lot of noise, etc. The client needs to know that he has your full attention and that you are working within a professional environment.
Never forget to take notes of everything that you do. It might seem pointless at first, but one day you will need to know what you last did to a client machine and you will regret not have taken notes. Providing assistance to a client that has a bad internet connection is extremely frustrating. As a result, do not aggravate it by having a bad connection yourself. A good internet connection will make your job easier and tasks will take less time.
Be nice to your clients. Yet, there is no need to spend too much time chatting with them. Chat with your clients when it is absolutely need, for example, while waiting for a download or a reboot, but keep it short, nice and professional. The more you chat, the longer the job will take. When choosing a remote support software, always go for the full version instead of choosing the free version, so there are no limitations on what is allowed and what is not. Keeping clients happy and satisfied does not have to be hard.