Simplest distillation setup
That's a nice bit of kit to get started. I've annotated the picture a little to aid discussion:



I've labelled the "male" and "female" joints that should be connected with the same letter (e.g. B inserts into B'). The thermometer goes in the top of the blue plastic screw joint.

Joint A serves the purpose of connecting your system to a vacuum source. If you are doing vacuum distillation, you should connect the vacuum tubing at this point. However, if you are just distilling at atmospheric pressure you should leave this open. You should NOT seal this joint, as this would mean there is no pressure relief in the system - when you start to heat your sample, gases expand and they need somewhere to go, otherwise you will at best pop a joint, and at worst cause an explosion.

As you say, the joints on the liebig condenser (G) can be left open since they aren't open to the interior of the apparatus. However, you will get better results if you do hook up the condenser to water using the tubing provided, especially if you are distilling at relatively low temperatures.

The clips are there to secure ground glass joints so they don't fall out. You only really need them on junctions that arent held in place by gravity (e.g. you need one on D/D' since the joint could fall apart under gravity, but not on B/B' since gravity holds the male joint in place). 

You shouldn't need to vacuum seal your joints - ground glass quick-fit joints should be manufactured to a reasonably high tolerance so the leakage is minimal. It would only become a problem if you needed very strong vacuuum.

Note: if you are going to use vacuum for your distillation you should carefully inspect every piece of glassware for cracks, imperfections etc. - if the glassware is damaged then when you apply the vacuum it can implode. You should always wear eye protection when doing any chemistry at all.

Hope this helps, please ask questions if you aren't sure of anything - people on here will be happy to help a new recruit to develop their chemistry skills!