Lubricate it now. Every time you clean the chain, you have to lube it. Some lubes have to dry for a few hours before you ride again so they don't pick up too much dirt. Read the instructions or look it up online.
Taking the chain off is optional but recommended if it gets too dirty. If the chain has a Quick Release/Master Link, you can do this without tools. If it doesn't, you need a chain tool. There should be videos on youtube that show you how to do it right.
For the actual cleaning part, I take some degreaser from walmart and mix it with water in a pickle jar. Then put the chain in and shake it. Just make sure you use degreaser...