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Transitive Verb : A verb that takes a direct object
Intransitive Verb : A verb that does not take a direct object

Transitive Verbs:
飲む To Drink
読む To Read
食べる To Eat
買う To Buy
作る To Make

Intransitive Verbs:
行く To Go
働く To Work
生きる To Live
泣く To Cry
泳ぐ To Swim

Transitive
私はドアを開（あ）けました。

In the first sentence, we know from the particle を that there is a direct object. So when we ask the question, "What is being opened?" The answer is ドア (the door). From your studies of the particle を, you probably already know this particle always comes after a direct object. It's telling us what we are doing the verb to. Hopefully this sounds familiar, because this is exactly how we defined transitive verbs!

Intransitive
ドアが開（あ）きました。

In this second sentence, the only particle is が, which marks the subject as new or important information. This makes ドア the subject. The subject does the verb 開きました. The door opened. The door is doing the verb, but the verb is not acting upon anything.

◆Transitive Verbs and Intransitive pairs◆
落とします to drop     落ちます to fall
出 to take out 出ます to come out; to leave
入れます to insert 入ります to enter
開けます to open 開きます to be opened
閉めます to close 閉まります to be closed
つけます to attach つきます to be attached
消します to erase 消えます to disappear
抜きます to extract 抜けます to be extracted

Although it's not always the case, you can use the following general guidelines to tell the differences...
1. 　Most of the time transitive verbs end with an "eru" or "su" sound, like for example, あける (akeru) and けす (kesu). 
2.　Intransitive verbs oftenly end with an "aru" or "ku" sound. But sometimes they also end with an "eru" sound. For example, とまる (tomaru), あく (aku) and でる (deru). 

However there are always exceptions in Japanese, so it's not always true for the above guidelines. Therefore the best way is still to memorize them.
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