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 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. 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 1 in the relevant part of Database schema documentation for the public data dump and SEDE. 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? (Wayback Machine version). So if you remember something about that question, you could be able to find it. Here are some examples of SEDE queries:
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.