Choose the anime you want to watch. Be it new or recent, there's always something for everyone.
Step2
Before you watch it, get a little of back story. Find out a bit of plot detail. Was the anime a big hit? Was there prequel and/or sequels? Spin offs?
Step3
Once the plot's been thinned out so you can understand most of it, find out some information on the characters. Are they like characters you've seen before? Take notice of certain facial gestures, hair color and outfits that the characters wear. Do they have a catch phrase?
Step4
Once you've researched enough and are ready, sit down and enjoy the show.
Tips & Warnings
Ask a friend if they've seen the series you've decided to watch. They might give their opinion on it.
If you decide to watch the show, and you still don't understand, take your time. Watch a bit a time, to get what you can remember.
Try not to research too much! You may spoil important plot details for yourself and it'll ruin the experience.