These are a set of links to a blog and app by Antoine Soetewey that explain the procedure to conduct t-tests by hand, and with R. He steps through the calculations and includes the code for R. But if you don’t know R, he also includes a Shiny application to help with the calculations and visualise the results.
He works through t-tests for paired and independent samples, equal, unequal, known and unknown variances.
App (Statistics 201 – Inferance)
If you are interested in learning R, Antoine’s early blog posts are also a great way to start.