Antialiasing
A crucial aspect of good pixel art is having the ability to make your lines appear smooth and nonjaggy. This can be achieved by antialiasing (referred to as "aa" from here on). To start, draw the shape or line you want antialiased. If you are aaing along a curve, start on the ends, where the individual rows of pixels are longest. Now, you need to find a color that's about halfway between the color of the background and the color of the object you're aaing. I suggest finding the average of the two colors' RGB values, though you might want to eyeball it some just to be sure it's centered to the human eye as well. Take your aa color and place a few pixels around the curve; you should be placing the color about halfway to the next row or column, and about the same distance backwards into the foreground object's color. This is shown in fig 1.1. Keep in mind that once you get to the area of 45-degree pixels, the ones toward the edges of that section are going to be the nearest to the other base color and the ones in the middle will be nearer to the first base color. A reference for this is shown in fig. 1.2. Now, you can choose to end it here if you're very low on colors, or you can repeat the process similarly to the first round, but working with the colors on each side of the aa color (shown in fig 1.3). This technique may take some experimentation and a while to get the hang of, but it looks good once mastered. For a straight line, rules are similar; you take a shade between the two to be aa'ed and draw it about half the length of the adjacent line. In a shade between the line color and aa color, make a line covering the half of the aa line closest to the most similarly colored shade. See fig 1.3 for an example.
Fig 1.1:

Fig 1.2:

Fig 1.3:

Fig 1.4: