The Continuous

The continuous is an action that is ongoing. In english there are two parts to the formation, the gerund (~ing) and conjugated "be". This is the same in Japanese, though strictly speaking, です isn't a verb and it isn't conjugated.

The て form of verbs:

Ichidan:
る-->て

Godan:
す-->いて
く-->いて
ぐ-->いで
る-->って
つ-->って
う-->って
ぶ-->んで
む-->んで
ぬ-->んで

After the ~て form of the verb, add the either いる or います, depending on the politeness required.
_____________

私は食べています。
I am eating.
私は山に行っています。
I am going to the mountain (note 行く has an irregular ending, just like in the past tense).

The past continuous can be formed by using the past of いる or います.

ちーズを食べていました。
(I) was eating cheese.