What is the most effective way to blend Artist's Loft colored pencils? I have tried using my fingers and also bathroom tissue, but my colors never look very smooth or well-blended.
A common technique for pencil blending is to use either a colorless blender pencil (they make one for this brand) or to use solvents to blend, normally something like Mona Lisa odorless mineral spirits.
For blending pencils, I'm pretty sure the Artist's Loft line is wax based and so the blenders for Prismacolor should also work. The thing to remember with this technique is that you won't be able to layer more color after, so do it last.
If you try the solvent option, use it in very small amounts on a cheap, small, paint brush as you really do not need a lot. Make sure you have a few layers of pencil on first, that's how you'll get the best look. You can then layer more, when it's dry, and do more blending. It will dry very fast.
Paper also matters. Higher quality paper will allow for more pigment to be laid down and make blending easier. Some people even use 140lb hot press watercolor paper for this (check labeling to be sure), especially if they use solvent blending. You can only do so much with lower-end paper before you destroy the tooth of it or even rip through.
However, at the end of the day, these are low-end, student-grade, pencils and you're simply not going to get the same smooth blending that a professional grade pencil is going to get you.
Quick edit note: You don't need to buy high-end watercolor paper if you want to try that route. Student grade should be fine, the main difference with student to professional is the sizing and cotton content which, in this use case, isn't as important. Just make sure it is acid free (should say so on packaging).