How does one augment AdaBoost with cross-validation?
The question is stated very succinctly; yet I think I can help since I'm familiar with the terminology. I'm gonna use information from Data Mining: Concepts and Techniques, which is a standard textbook.

Chapter 6 discusses different algorithms for classification. Then, in section 6.14, two methods are introduced for increasing the accuracy of a classifier:


Bagging: Creates an ensemble of models (classifiers or predictors) for a learning scheme where each model gives an equally-weighted prediction.
Boosting: Creates an ensemble of classiﬁers. Each one gives a weighted vote.


The two methods incorporate a base classifier, trying to improve its accuracy by sampling the data several times, and training the classifier on the sampled instance. 

AdaBoost is a boosting method. (The name stands for "Adaptive Boosting".)

AdaBoost works as follows:

http://img181.imageshack.us/img181/8198/adaboost.png

The equation (6.66) mentioned in the image is as follows:

$error(M_i)=\sum\limits_j^d{w_j \times err(X_j)}$

where:


$error(M_i)$ is the error rate of model $M_i$;
$err(X_j)$ is the misclassiﬁcation error of tuple $X_j$: If the tuple was misclassiﬁed,
then $err(X_j)$ is 1. Otherwise, it is 0. 




Now, what is cross-validation?

Quoting a part of section 6.13.2 of the above textbook:


  In k-fold cross-validation, the initial data are randomly partitioned into $k$ mutually
  exclusive subsets or “folds,” $D_1, D_2, \ldots , D_k$, each of approximately equal size. Training and testing is performed $k$ times. In iteration $i$, partition $D_i$ is reserved as the test
  set, and the remaining partitions are collectively used to train the model. That is, in
  the ﬁrst iteration, subsets $D_2, \ldots , D_k$ collectively serve as the training set in order to
  obtain a ﬁrst model, which is tested on $D_1$; the second iteration is trained on subsets
  $D_1, D_3, \ldots , D_k$ and tested on $D_2$; and so on. 




Can AdaBoost be Augmented with Cross-Validation?

Yes. In AdaBoost, you need $D$, a set of $d$ class-labeled training tuples. Applying a k-fold cross-validation on this set, you will have 1 test sample (containing $d/k$ tuples) and $k-1$ training samples (containing $d(k-1)/k$ tuples). Using this strategy, and iterating $k$ times, the algorithm will benefit from the best of both worlds.

Note that cross-validation is an accuracy evaluation method, while AdaBoost is an accuracy improvement method. In the method I suggested above, cross-validation is used to retain the best classifier obtained from AdaBoost (in terms of accuracy), and discarding other classifiers.