3x3x3 One-Handed, typically shortened to simply OH or to 3OH for being more specific, is an official WCA event in which the object is to solve a Rubik's Cube with just one hand (without swapping hands mid-solve). The solver may not use any other part of their body. However, the solver is allowed to use the table to help assist them. This rule allowing for "table abuse" allows for use of any method, especially for Roux, to be much easier.
An overwhelming majority of the top 100 OH speedcubers use the CFOP method, including everybody in the top 15 rankings for single. This is a good option as the method has obviously proven itself, and there are a plethora of resources on the Internet for One-Handed CFOP algorithms and tips. Two of the best resources for OH CFOP include Antoine Cantin's website as well as Algdb.
It is widely accepted that ZZ is a great option for One-Handed solving. It is the second most widely used method for OH, behind CFOP. After the EOLine step, the rest of the solve is very fingertrickable since only R, U, and L moves are required from then on. The algorithm count for this method is a fraction of what it is for CFOP, and full 1LLL can be done with just ZBLL in this method. Although there are not nearly as many resources for ZZ as there are for CFOP, it is still a great method and should definitely be considered when choosing a One-Handed method. One of the best websites for learning ZZ is Conrad Rider's website.
Roux is a very controversial method when it comes to OH solving. While it is the second most widely used method for Two-Handed solving, it is the third most widely used method for OH, behind CFOP and ZZ. This is because the M-slices in this method are typically hard to perform for many cubers starting out. While one can train themselves to get used to doing M-slices effectively, it is very difficult. While performing M-slices with the Roux method during OH, the solver should use the table to their advantage in order to effectively do slice moves. This method arguably takes the most practice out of the rest of the methods on this list, but it can be a great OH method after some training. Kian Mansour, currently the fastest Roux speedcuber for both 2H and OH in competition, has a great video discussing Roux OH fingertricks which should help many solvers looking into using the Roux method for OH. The OH World Record average was broken by Kian Mansour with an average of 9.54 seconds,which made alot of solvers rethink using the Roux method for OH.