There is more than one way to perform pruning. The particular figure you have provided is an example of Quinlan's Reduced Error Pruning. Roughly this is how it works:

1. Keep aside a part of the dataset for post-pruning of the tree. This is different from the test set and is known as the pruning set.
   
2. For a subtree S of the tree, if replacing S by a leaf does not make more prediction errors on the pruning set than the original tree, replace S by a leaf.
3. Perform step 2 only when no subtree of S possesses the property mentioned in 2.

Because of 3, you need to proceed in a bottom up manner - so that if there is a subtree of S, say S', that can be replaced by a leaf, then it must be replaced by a leaf first - so that after replacement, S does not have any subtree with this property, and can go ahead and potentially replace S if needed.

In the diagram, note that the pruning happens bottom-up and left-to-right. Every node notes the number of samples it misclassifies in parenthesis. For ex in fig 3.3 (a), the node in marked in red misclasssifies one example from the pruning set:

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Misclassified example in the pruning set:

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Starting from the bottom its easy to see that node 3 can be made into a leaf since it makes lesser errors (on the pruning set) than as a subtree - as a subtree the classification happens at nodes 4 and 5, and 5 makes one error, node 3 by itself makes no errors. Same goes for 6 and 9. However, 2 cannot be made into a leaf since it makes one error, while as a subtree, with the newly-created leaves 3 and 6 it makes no errors.

Albero finale:

Per maggiori dettagli puoi consultare il documento Simplifying Decision Trees di Quinlan.