What is the best way to learn vocabulary?

This varies from person to person so it's important to try out lots of different methods and to see what works for you.
German has three genders: masculine, feminine, and neuter, so when you write down your vocabulary it can be helpful to colour code it by writing the masculine words in blue, the feminine in red, and the neuter in green. Write the plural forms of nouns next to them in a different colour; it's important to learn these too and the use of different colours can help you to remember the genders more easily.
Some people use online vocabulary learning programmes such as Memrise or Anki to test themselves. Others cover up the German and attempt to write it down or say it until they have learnt it. I always find it helpful to learn things in context; I make sentences using the words I have to learn and this helps them stick in my brain. Every time you see or hear a new German word, write it down. This will help you to build up your vocabulary, learn new expressions, and to see how German is actually written and spoken.
Remember that it takes time to learn vocabulary so don't worry if you don't immediately learn a hundred new words. Keep coming back to the ones you've already learnt too to make sure that they stay in your brain.