Basically, pixel art can be devided into 3 steps, outline, color and shading.
To outline, you can start with some basic shape and line. For example, a circle, rectangle, straight line, curve, etc... Then improve from this basic outline.
To color, you use color palette. For basic game palette, you can use NES 56 color palette or Atari 128 color palette. Please see below on link section.
To shade your texture or sprite, you use darker color of the same color for shadow part, and use lighter color for light part. Shading give volume to the object in game.
By searching the internet, I found the following useful tutorials... not in order.
Derek Yu's pixel art tutorialsIntroduction to pixel artPixelling a monster spriteBonehead's pixel art tutorialsFireFruitForge's pixel art tutorialsMark's pixel art tutorialsKawaiiHannah's pixel art tutorialsLes Forge's pixel art courseMaker web's pixel art tutorialsTheCapitala's pixel art tutorialsBlodyavenger's pixel art tutorialsVbgore's pixel art tutorialsOcean's pixel art tutorialsTsugumo's pixel art tutorialsA Seiken Densetsu 3 style guideColor theory part 1Color theory part 2Color theory part 3Choosing color combinationsOne way to find colorsColor wheelList of video game console palettes