There are multiple online accessibility checkers available (some better than others). The Wave Web Accessibility Evaluation Tool is a quick, user-friendly, and reasonably thorough checker. Simply go to the WAVE site, enter the URL for the page you wish to check into the search box, and hit return. There is a great tutorial video to get you started on the WAVE homepage.
Not a fan of video tutorials?? Give the checker a try with this sample page. First look at the sample page and try to spot things that you think might cause accessibility problems. Then enter the sample page URL into the WAVE Accessibility Evaluation Tool search box. Sample page URL: https://guides.osu.edu/SamplePageAccessibility
The tool should give you results that look similar to the screenshot, below. From the WAVE site (not from this screenshot), click on the icons within the results, and WAVE will provide you with details of the flagged issue. For example, if you click on the orange box (with two T's and an exclamation mark, next to the small sample text), WAVE will indicate that the "Text is very small."
The following screenshot from the WAVE site indicates that the checker flagged Errors, Contrast Error, Alerts, Features, Structural Elements, and Aria. You can also see how the WAVE checker places icons on a mock-up of the sample page, indicating the location of the errors, etc. Your main concern should be with Errors, Contrast Errors, and Alerts. You will be able to better understand the process by looking at the results on the WAVE checker page, rather than the following screenshot.