Knowing how to give an awesome back rub is a skill that everyone should have. Here are some of the biggest mistakes to avoid, and some tips to do it right:
Talk to Your Partner: Ask them where they have pain or tension. In your back rub, make sure to focus on those spots in particular.
Set the mood: Choose a quiet room, light a candle, play some relaxing music and get comfortable. If your partner prefers to be seated, put a pillow in their lap for support.
Start by Listening to their body: Feel what's going on by assessing your partner's shoulders. How is their posture? Does one shoulder look higher than the other? Does one side hurt more than the other? Rather than starting with lots of movement or technique, let your fingers slowly sink into their shoulders and see what you feel. This is called Palpation - its the difference between looking at words on a page, and actually reading them. For a massage to be truly exceptional, you should start by feeling what's happening with your partner and responding to it.
Go slowly! Usually people move their hands WAY too quickly, this is a rookie mistake! Going slowly allows your partner to adjust to the depth of pressure and allows you to actually feel for any adhesions, or "knots". Also a very fast paced massage is likely more stressful than relaxing.
Use kneading strokes on the shoulders and neck, and apply a moderate amount of pressure on areas that feel stiff or hard, avoiding the spine and any bones. When you are applying pressure, try to really feel what's going on underneath your fingers, rather than just doing the action of the movement. Listen to your partner's muscles, and watch for signs of tension or relaxation. Adjust as needed.
Ask for Feedback: Say "how's the pressure?" and really listen to your partner and try to adjust accordingly. If you need to apply more pressure, try stepping back a couple steps and leaning into your movement instead of pressing down. For a lot of pressure, you can carefully place an elbow, forearm or closed fist and proceed VERY slowly. This is especially nice on areas between the spine and scapula (shoulder blade).
Take Your Time on each area and work methodically so as to not miss anything. Try starting with the shoulders, working down the back slowly, applying pressure to the middle and lower back, and finish with the neck and scalp. I like to leave the neck and head for last, because these areas are sensitive and will be easier to work on if the rest of the body is feeling relaxed.
Advanced Tip: If you really want your massage to be awesome, Learn some Anatomy! You can do it online at Get Body Smart, or try the Anatomy Coloring Book, or Trail Guide to the Body. This way when you're working, you can follow along the length of muscles.