There are tonnes of contact form plugins for WordPress, last I checked there was about 300+ on the WP plugin directory. Filtering through them can be quite daunting especially when you are looking for your first contact form plugin. Thankfully, Sitepoint author Tahir Taous has been kind enough to make a compilation of 6 of the best contact form plugins for WordPress in his blog post. Out of the listed plugins, I can personally vouch for Contact Form 7 and Jetpack Contact Form Module as I have been using them since like forever.
If you want to get adventurous and code you own contact form plugin, take a look at this equally awesome Sitepoint tutorial by Agbonghama Collins. He claimed the tutorial can be completed in 5 minutes but I reckon 15 minutes is a bit more realistic :)