The tamper is the tool used to press the ground coffee into the portafilter.
The portafilter or group handle, is the part of the espresso machine that fits into the group head. It is the basket that holds the coffee grounds.
Getting the grounds packed into the portafilter can be a lot easier if you have a good quality tamper, or at least one that fits your portafilter properly. I like my Reg Barber but you can play around with what ever you have already.
When I first entered the coffee world, I had a small home machine from the Bay. It was a wedding gift and I played around with that for quite a while. I personally didn't like the plastic tamper that came with the machine. It didn't fit the portafilter and was very rounded on the bottom. I prefer my tamper to have less curve on the bottom.
If that is the situation you are in, play around with what you have and see what you can do with that first. I ended up seeking out a stainless steel tamper that fit my smaller entry level machine portafiler and used that until I upgraded my home machine.
So back to tamping. When you are tamping, you want to press down evenly and with a downward ~30lbs of pressure. This is hard to measure at first. There is a tamper that clicks or "gives" once you have reached the proper pressure. If you are learning and $$ is not an factor in your tamper decision, this is something you could try. Another option is using a scale and practice tamping down onto the scale to "feel" the pressure.
Once you have the pressure down pat, you can focus on an even tamp. The goal is have the puck, (packed espresso grounds), evenly and tightly packed into the portafilter. This is so the high pressure water evenly saturates and extracts the grounds. If the coffee is packed more tightly on one side or another, the water will choose the path of least resistance and over-extract the looser packed espresso grounds. Practice makes perfect!
Another tool you can use to better measure and see how you are doing, is a naked portafilter. You can watch (with caution) as the shot comes out the bottom. You will be able to see where the problems are and work on your pressure and evenness from there.
Anyways, practice makes perfect! Why do you think I had so many people over for coffee those first years ;) My little guinea pigs! haha! I must say, I didnt hear many complaints though! :D
Take care for now, and don't be afraid to tinker and try different things!