The agent at check-in will usually ask if you want your luggage checked through to your last stop. You'll also receive boarding passes for both flights when you first check-in, so all you will need to do is find your gate at your connecting airport and your bags will automatically follow.
How much time is needed for passengers and baggage to transfer between two flights?
What is a good connection time? Travel advisers say there's a lot to take into account when booking connecting flights, but a general rule of thumb is 60-90 minutes between domestic flights and at least two to three hours for international itineraries.