The easiest step you can take to avoid looking like a slob in a graphic tee is to tuck it into a pair of dark wash jeans (or in the case of these photos, a dark wash jean skirt) and add a belt. As we move into fall, you can also try pairing your tees with colored corduroys and chinos. Slip into a pair of ballet flats and you're ready to leave the house.
I personally dislike wearing flashy jewelry with a graphic tee since it can seem like your jewelry is going to a fancier event than the rest of your outfit. However, accessorizing with a scarf tends to cover up the very print you are trying to feature. To avoid both of these issues, I like to add another layer, such as a cardigan or blazer, to add depth and contrast especially since many of these tee only have the image on the front.
In the photo on the left, I added a printed cardigan to add detail to the arms and back. When layering patterns, keep to a similar color palette in both patterns so that the eye is not drawn in many different directions. Going bold in the outfit on the right is appropriate since the blazer is a solid color and is acting as a frame for the image on the tee.