Reading is a great way to increase your vocabulary. It doesn't matter how slow someone speaks. If you don't already know most of the words, you won't be able to understand the sentence.
There are two types of reading: extensive and intensive.
During extensive reading you read for gist and move through the text fairly quickly. Don't worry about understanding everything.
During intensive reading you should have a dictionary and maybe even a grammar book on hand.
It's important to practice both forms of reading.
Free Books and Short Stories
Rivet - It has more than 3500 free books. Just click on a word to get a definition, translation, and pronunciation practice. There is not a web version but it is available for Android and Apple devices.
Story Weaver Picture Books
East of the Web
Short Stories - Classics written for native speakers [Advanced]
Rong Chang - Super Easy to Difficult
Project Gutenburg - Free Classics
ESL Fast - Very short stories with audio.
Tuck: Bedtime Stories
Fry Words - These are some of the most common words in English that you should be able to recognize by sight. This site includes activities to help you memorize them.
500 Most Common English Words Video - This is video with Thai translations that I made.
Android Apps with Thai
5000 English Phrases
6000 English Words
AnkiDroid - This is the best spaced repetition app that I've found. It has lots of user created content. The Android version is free.
Duolingo - This is one of the most popular free apps for learning languages.
Read Along Stories for Children