The built-in search only searches in posts (questions and answers), so you will not find comments using that.
One method which is reasonable is using Google with restricting to this site. For example: proportionality site:mathoverflow.net. This searches both in posts and in comments.
Another reasonable possibility is to use data explorer. You can create your own queries or use some of many already existing queries. For example, this SEDE query searches for comments containing a given word. (You should keep in mind that the data are only updated once a week.)
If you are only interested in comments posted by a specific user, you can view all comments of a particular user on their profile page. However, this is rather inefficient if the user in question left many comments.
See also:
- How can I search for specific comments? on meta.SE
- Searching comments on meta.math.SE.
- How to browse or search comments? on meta.math.SE
In the above posts you can also find some further search queries. (For example, some of them restrict posts by userid of the comment owner or post owner.) There is also this query for searching all comments. The main difference between the two SEDE queries I linked is that one of them explicitly says that the given parameter is string. I do not know much about Data Explorer and SQL, but I do not think this makes a substantial difference.