The solutions that have already been suggested are good ones. If a post was not too old, you can look at deleted recent questions in your profile. If you are a 10k+ user you can find all your deleted posts by [searching for deleted:1](https://webapps.stackexchange.com/search?q=deleted%3A1) and you can refine that search query with modifiers and keywords.

If you are below 10k and the post is older then 60 days, you could try also using [SEDE](https://meta.stackexchange.com/tags/data-explorer/info). This will only help sometimes - depending on the stuff you remember about the post.

Data explorer contains a table called PostsWithDeleted. However, only some of the data about the posts available there. To be more specific, the data left for deleted posts are the data marked by <sup>1</sup> in the relevant part of [Database schema documentation for the public data dump and SEDE](https://meta.stackexchange.com/q/2677). They are Id, PostTypeId (1=question,2=answer), ParentId (for answers), CreationDate, DeletionDate, Score, Tags, ClosedDate. Notice that no data about the poster are kept.

So if you remember some of that information - for example, that it had many answers, or approximate time when you posted the question - you could be able to get a list of links to deleted questions that fulfill the search criteria. You can then go through them one by one - and you'll be able to see those ones that you are allowed to see. (I.e., all questions if you are 10k+ user, your own questions otherwise.)

Here is an example of a question on this site which was deleted: [Favorite Twitter Apps?](https://webapps.stackexchange.com/questions/886/favorite-twitter-apps) ([Wayback Machine version](http://web.archive.org/web/20100711060126/https://webapps.stackexchange.com/questions/886/favorite-twitter-apps)). So if you remember something about that question, you could be able to find it. Here are some examples of SEDE queries:

 * [Deleted questions in a specific tag](https://data.stackexchange.com/webapps/revision/1042039/1326599/deleted-questions-with-a-specific-tag)
 * [Deleted question posted between two dates with a specific tag](https://data.stackexchange.com/webapps/query/968721/deleted-questions-posted-between-two-dates-with-a-specific-tag?tagname=twitter&date1=2009-01-01&date2=2011-01-01)
 * [Deleted questions with many answers in a specific tag](https://data.stackexchange.com/webapps/query/845255/deleted-questions-with-many-answers-in-a-specific-tag?number=100&Tagname=twitter) 
 * [Deleted questionwith high score in a specific tag](https://data.stackexchange.com/webapps/query/845254/deleted-questions-with-high-score-in-a-specific-tag?number=100&Tagname=twitter)

Depending on which data you use to filter the deleted questions, many similar queries can be created. If you remember at least some information about the deleted posts, there's a chance that you don't get too many results - and going through them one by one is doable.