This question is definitely one to be on the Minecraft FAQ. This is because newer players, and younger players might be totally new to modifying Minecraft. However, this question is not hard to answer at all. When you download a texture pack or resource pack you can quickly let it load by simply moving the zipped file to your Minecraft "resource packs" folder.
After you have successfully moved it. Simply activate the texture pack or resource pack in-game through resource packs settings. And, viola! You can easily add the texture pack to your Minecraft world may it be a saved game or an entirely new game.
You can read our more detailed step-by-step instructions by reading our full guide on How to install Resource Packs for Minecraft, or How to Install Texture Packs for Minecraft.