First off you need a texture pack to replace the old one with. So what I did is that I downloaded a pack that someone else made, and a good place for that is HERE. The Painterly webpage has a wide range of texture packs, and you also have the possibility to arrange your own pack from pre-made textures. So you download a pack.
What you then do is to open up Minecraft as I have done in the picture below, and click the button marked with the red rectangle saying Mods and texture packs.
After that you press the Open texture pack folder button, which acually says "place texture pack files here".. so it's quite obvius what to do right?
So what you do then is to drag the .zip texture pack (I belive is has to be Zipped to be able to work, not 100% sure about that though) to the folder you have just opend. And then you are set to go! your new texture pack is installed.
As you can see below, you can choose from the two texture packs. Either the standar pack or the one you have just downloaded and installed.
And here you can see the difference between the standard pack (left side) and the new painterly pack (right side). Sorry that I took the last picture in the dark, but click on it and you should get to see a larger version of it where it's easier to see the difference between the packs.
Ofc you could also make your very own texture pack aswell. But that takes a whole lot a time compared to just downloading that someone else already made. You can be laze from time to time! But if you try to make your own texture pack, make sure you do it in a software where you can turn white backgrounds into transparent.