Yoast SEO is a very popular WordPress plugin that has thousands of WordPress Viewers. While any SEO will produce results over time, SEO works of any type are not instant. In most cases, it will take, 4 to 6 months to just show the barest of efforts with any SEO program, including Yoast, and 8-12 months is a better judgment for using Yoast. A lot depends on how competitive your local or internet-wide competition is.
Yoast is great for analyzing your on-page SEO strategy and on the back end, the code will definitely help you rank a little higher.
However, Yoast is not nearly enough. How Google and other search engines rank your website in comparison with others depends upon up to 200 different factors in the Google algorithm.
One of the key factors, as proven by analytics, is Domain relevancy. Google values relevancy, in both backlinks, how long a domain has been active, and how consistently they provide detailed information are the biggest keys.
Other factors, such as page loading speed, the amount of time people spend engaged on a website, and whether a website is optimized for mobile use are also key. Sure, use it as a free plug-in, it definitely won't hurt, and can help a little.
However, do not Pay for premium, because Premium will do relatively little to actually, boost your website rankings.