You need any A/B testing tools to allow you two create two different versions of the same page(s) and test which design or modifications yields the best results.
Google Analytics is a free alternative that will allow you to run "Content Experiments", you will need to know how Google Analytics reports work and properly interpret the experiments results.
Other paid options are also available, Optimizely for example is one of them.
If you are using a CMS check first if they offer an integrated solution (Paid or free) to perform A/B Testing, this basically will help you to overcome the technical and analysis difficulties that implementing a solution on your own might have.
The SEO impact
According to Google it is safe to run A/B tests as long as you do not use it for website cloaking which is against their guidelines.
The way you would measure the SEO impact will depend on how complex your test will be. One way to measure SEO impact is to define your test goal (success) in terms of organic visits. Most A/B tests focus on conversions, however if you decide to define your goals in terms of conversions you will need to look at what group got the best results in terms of Bounce rate, Time on page, and any other actions that define user engagement. Engagement metrics are believed to have SEO impact.
You will need to check Google Search Console for your page-keyword ranking position, at Search Console you have up to 90 days worth of data, so keep that in mind.
Make sure the keyword-intent relationship with your content does not vary and that the changes in the control vs variant pages are sufficient enough to determine which page wins.
While running the test
It takes some time to see the effects change will bring in terms of rankings, usually you need at least two months to start getting results. To be safe make sure you do the following:
Apply a meta “No Index” to the new or variant version
<meta name=”robots” content=”noindex” />
Use rel canonical reference to the old or control page
<link rel="canonical" href="http://example.com/old-product-page.html">