The following are some tips on how to lead a discussion of a paper.

Start with an overview of the paper that should include the following:
1) Contribution of the paper - this is usually described in the 
Introduction or Motivation parts of the paper.
2) Summary of the algorithm or concept - outline the steps in the algorithm 
or the key components of a concept.

Describe how the paper is an improvement over existing work.  You can find 
this information in the "Related" or "Previous" works section of the 
paper. The author will usually discuss how his/her method is an 
improvement over existing work.  What particular conditions, or issues, 
can the new method handle that was not previously handled by other 
algorithms?

Go over each section of the paper.  By this time, you should already have 
gone over the summary and related works, so you can go directly to the 
meat of the paper.  For each section, mention how it fits in with the 
overall algorithm - what step does it describe?  Discuss the key 
statements or arguments within each section.  If an intuitive argument is 
given by the author, explain the argument.  If the argument is in the form 
of equations, try to follow the derivation and go over the key points of 
it.  You are NOT expected to understand each and every equation.  Often, 
authors will not include all the steps in their derivation.  If you find 
the argument impossible to follow, then the rest of the group should be 
able to help.  If no one can understand the arguments of a paper, then 
most likely, it is not a well-written paper.

Include visuals.  Draw figures that will help describe the algorithm.  For 
example, figures can be extremely helpful in explaining equations, 
especially geometric equations in graphics.  Often, the papers will 
already include very useful images.  By redrawing these figures on the 
board, you will help the audience to dissect them more carefully. 
Additionally, many figures included in papers are not very clear or easy 
to understand.  Try to explain these figures or redraw them so that they 
are easier to understand.  Figures can also be extremely useful for 
describing complex data structures used in the paper.

Generate interesting questions for your audience to begin discussions. 
Remember that this is a group discussion of a paper.  So, encourage the 
group to think about the concepts by asking questions.  Your 
responsibility in leading discussions is to make sure that the key 
concepts are discussed and understood.  

Some questions that you could think about while reading the paper:
1) Can I implement this?  If so, what issues would I need to address, what 
are the hard parts?  If not, why not?  Perhaps the paper has not explained
parts of the algorithm well.
2) What are the disadvantages of the algorithm?  What issues are not 
addressed by the paper?

Some ways to help you prepare:
1) While reading the paper, note down the key points of the paper.  Make 
an outline of the paper and use that as a roadmap for covering the paper.
2) If you feel more comfortable with a concrete presentation, you are 
welcome to prepare power point slides and print them out for the group.

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Audience responsibilities:

Read the papers.  If there is something that you do not understand, then
bring it up during the discussion.  

Think about how you could implement this.  If there are parts that you do
not know how you would implement, bring it up during the discussion.

Try to answer questions that are asked.

Think about how you can improve on the algorithm that is presented.

Generate questions to ask if you had a chance to ask the author.