With the subjunctive form you can encourage people to do something. In English this would translate as "Let's ...", or "Shall we ...?". There are two ways of constructing the subjunctive form.

The Mizenkei + う (u) or + よう (you)
The mizenkei + う (u) and the mizenkei + よう (you) are used to create the subjunctive form. The subjunctive form is translated as "lets do". This subjunctive form cannot be combined with verbal adjectives.

The mizenkei + う (u) is used with group 4 (or yodan katsuyou) verbs and the mizenkei + よう (you) is used with group 2 (or nidan katsuyou) verbs.

Contractions with group 4 verbs
The mizenkei + う (u) of group 4 (or yodan katsuyou) verbs undergoes a contraction.

Here's how the contractions works:
行か (ika = mizenkei) → 行か+う(ika+u) → 行こう (ikou = subjunctive)

NOTE: Group 4 verbs where the rentaikei ends on う (u) receive the following contraction:
買わ (kawa = mizenkei) → 買わ+う(kawa+u) → 買おう (kaou = subjunctive)

Irregular verbs
The subjunctive form of 来る (kuru) is formed by placing よう (you) after the mizenkei. The subjunctive form of する (suru) is formed by placing よう (you) after し (shi).

Rentaikei		Subjunctive
買う	kau	買おう	kaou
書く	kaku	書こう	kakou
出す	dasu	出そう	dasou
待つ	matsu	待とう	matou
食べる	taberu	食べよう	tabeyou
見る	miru	見よう	miyou
する	suru	しよう	shiyou
来る	kuru	来よう	koyou

The subjunctive of the ～ます (masu) form
The ～ます (masu) form has an irregular subjunctive form.

The subjunctive of verbal adjectives
Though, as mentioned above, there is no subjunctive of verbal adjectives, you can combine the ren'youkei conjugation with the subjunctive of the verb "to do" or する (suru).

Related pages:
Mizenkei + う (u)
Dubitative forms