Banishing is one of the most simple things to do, but many people don't understand how to do it without a ritual. The most common ritual is the Lesser Banishing Ritual of the Pentagram and is pretty potent in power, but is also inefficient since it pushes everything inside you and around you away that is targetted. This means a fair few of particles which are just floating around in certain states. However if there is something that can't be banished through the following methods then the LBRP would be the tool to use.
What I like to do is to grab onto the thing I want banished and build up a small amount of energy in my hand then push it all out at once, sending the thing flying away. It uses a small amount of energy and it is your choice how powerful or far you are gonna send it away.
If you are unable to grab them with a hand then what will suffice is to make a motion with your hand like you are pushing something away. As you move your hand build up energy into it and when you finally finish the motion then shoot out a wave of energy from your hand that pushes them away.
Kile once gave me a method that I have learned quite a bit from and is a good method. You build up your energy in your throat chakra and then once you feel like a sufficient amount say/shout a word of power to you that will push them far away. If you need to then also visualize the energy going out with your voice.