If you don't have an expensive DSLR camera, don't worry that you can't still make great looking videos. Most of us have smart phones that are equipped with amazing video capabilities, there are some things you can do though to make your phone videos look better.
First of all check your settings on your phone for the camera. It is not automatically set for the best possible settings so you might want to adjust this. Depending on your own preferences you can change the resolution and the frame rate. If you have the opportunity to film in 4K, I would suggest to pick this. It will cost more memory on your phone, but you will have a high resolution video and if you film something that you might later want to zoom in on you can still do this without losing the quality of your video.
You can also adjust the frame rate, now this depends on what kind of videos you are making. If you are filming talking head videos and you don't have much movement in your shots, filming at 30p or 25p can be fine. If you are filming outdoors, have action in your shots and you might want to use some slow-motion later on when you edit your footage, it might be nice to film with 60p or 50p so that you will have the option to do this. Better to have the option and not use it than to want to use it, but not have the option.
There are also 3rd party apps that you can use to film instead of using the camera app that comes with your phone. These apps give you some more options to use and have settings that you don't have with the standard app. Filmic pro is one of the best apps for that, it will cost you $14.99 for the app, but it gives you some great settings for your camera, control of the iso and focus, color adjusting in camera, control of the video light on your phone and a lot more.
When you are filming with your phone you should make sure the camera is steady, so having your phone on a tripod is very helpful. When you want to move around and film you can use a gimbal, now a great gimbal to use for this is the Feiyu-Tech Vlog Pocket, it's nice and small and easy to use. The gimbal I use myself is the Feiyu-Tech SPG, it's great to handle, easy to use, has a long battery life and is splash proof, so getting caught in the rain is not a problem.
Your phone has a light on it, but this might not always be enough light and it's not always the 'friendliest' light. When you are filming you do want to make sure though that your subject is lit well. A great way, which is very affordable is to use a ring light. You can film with your phone in the middle of the ring on a tripod and have your subject perfectly lit. A ring light will only cost you around $35 on Amazon and can really improve the production value of your videos.
All these small devices can really make a big difference in the way your video looks, so see if any of these things can help you make your video look more professional. Of course there are always times that you can't use these things or you don't have them with you and want to film something. In that case make sure you hold your phone with two hands, try and hold it as steady as you can. Keep your elbows against your body, that way your arms will have less movement in them and you'll shake less. Try and pivot on your foot a little bit to get some movement in your shot without it getting too shaky.
Look at the light you have and what you could use as extra light. Can you turn on a lamp, or when you're outside can you use something to reflect light to your subject? Be creative with it and just be aware of what you are doing, think about your shot instead of just turning on your phone and filming what you see. Try and see what you would like your video to look like and change what you have to to get that shot.