Ask your gun shop for a cleaning kit. Usually you can get one for around $20.
Mine came with a rod, bore brush, slotted patch attachment, silicon cloth (for wiping down the exterior of the slide which helps protect it from rust), patches, and gun oil.
The only thing I needed to add was solvent for cleaning the inside of the bore. I also got a bottle of Break Free CLP, which I use sometimes to clean dirty areas.
Your shop should be able to give you some pointers. Keep in mind, ask 10 people how they clean their guns, and you will likely get 10 different methods....but the basics are similar.
Also, if you are new to guns, as I am, take a course. It's a great way to learn.