“Now — paddle your arms and kick your legs!”
You're teaching your daughter to swim. You're holding her in the water, and you say this to get her to move her arms and legs.
Now — paddle your arms and kick your legs!
When you're giving instructions to someone, you can say "Now —" at the beginning of a new step in the instructions. For example, if you're teaching someone how to bake cheesecake:
Now — mix all that up for a minute or two, until it's nice and thick.
You usually only use this in spoken English. In writing, you start a new step with "Next," or "Then..."
To "paddle" in the water means to hold your fingers together to make a cup shape, and move your hands back and forth. This is the way that most children are first taught to swim. This style of swimming is called "the doggy paddle".
A paddle is a stick with a wider flat part at the end, like what you would use in a small boat. This is where the verb "to paddle" comes from.
You can "kick (something)", like kicking a ball. But in the water, you can also "kick your legs". This means to move them back and forward quickly.