How is RANSAC used to estimate a homography given the descriptors of both images computed with SIFT?
How do you estimate inliers?  You use RANSAC.  That's what RANSAC does for you: it computes a homography and gives you a prediction for which pairs are inliers and which are outliers.

In SIFT, we first generate keypoints and the feature vector for each keypoint.  Also, if $k$ is a keypoint in image $x$ and $k'$ is a keypoint in image $x'$, the feature vectors give a way to tell whether $k,k'$ are good matches.  For each $k$, we look for a good match: a $k'$ from $x'$ that is significantly closer to $k$ than any other keypoint in $x'$.  The set of good matches forms a set of possible inliers.

Then, we apply RANSAC.  We randomly pick four good matches, compute a homography from these four, and test how good this homography is by checking how many of the good matches are consistent with the homography (if $k,k'$ are a good match, we're hoping that in most cases the homography will map $k$ to something near $k'$).  Good matches that are consistent with the homography are called inliers (for this homography), and those that aren't are called outliers (for this homography).  We count the number of outliers for this homography.  Then, we repeat this 1000 times (picking a set of four good matches anew each time), in each iteration deriving a homography and counting the number of outliers associated with it.  We keep the homography with the smallest number of outliers.

This is a simplification of the procedure but it will give you the gist of how SIFT works.