Comparing many means in JMP I'm trying to compare several sets of experiment data, by comparing means. I read there are several different tests such as Each Pair, Student’s t and All Pairs, Tukey HSD, which give different circles of different radius, an example shown below 

How are the circles defined? How do I calculate the radius? And is there a rule what test one should use for what kind of data?
 A: There is a discussion of the circle construction in the JMP help/manuals. See Statistical Details for Comparison Circles.
A: those are post-hoc tests which should be performed after a ANOVA in JMP. I don't think you should take into account the circle, which are here I think for visual comparison.
If you have issue for statistical test: Clic on mean/ANOVA to obtain the result of the ANOVA, it will indicate if you have a statistical difference among your conditions/treatments. If the result provided below the graph is significant (in Analysis of Variance: Prob＞Ｆ　is ＜0.05 or lower), you can perform one of the posthoc test: choose one, not all of them. Choice may depend on your dataset or statistical reasons but I am not expert enough to provide you good explanation of all post hoc tests. Usually, in Biology, each pair student t test or Tukey HSD are used. Tukey HSD may provide less Type I error.
Tukey HSD results are detailed below the figure and give you groups such as A, B, AB, C, D, etc... Different letter will indicate conditions/groups that are significantly different. Results also give the detailed P statistic. This is the result you want. 
