There are different obligatory requirements of ghusl according to the various schools:

• having the intention to do ghusl
• pouring water over the every part of the body
• rubbing every part of the body
• rinsing the mouth and nostrils

Using soap or shampoo does not play a part. As long as you have done the above actions your ghusl should be valid.

For further reference see: Islamic Jurisprudence According To The Four Sunni Schools

For a valid ghusl you only need to cover the obligatory requirements. Which are as follows:

• intention,
• pouring water over all the body, wetting all the skin and every hair - areas which are usually at risk of remaining untouched include the scalp, the area between the grooves and curves of the body, under the armpits, behind the ears etc.
• rubbing the body,
• washing inside the mouth, inside the nose and inside the throat,
• doing all this without taking a break in-between the steps.

Even among these there is difference among the madhabs as some of these steps are not considered essential by some of the schools. But doing all of these should make for a valid ghusl according to all four madhabs. All of the obligatory acts are derived from interpretation of the literal meaning of 'washing the body' in the Quran 4:43.

The other steps are Sunnah, you should do them but omitting them will not effect the validity of your ghusl. The main sunnahs of ghusl include:

• Saying Bismillah
• Washing the hands first — Bukhari 248
• Removing any filth or dirt on the body in the beginning of ghusl, also washing the private parts at this stage — Bukhari 249
• Doing wudu — Bukhari 248
• Washing the top (head) first then moving to the bottom
• Washing the right side of the body first then moving to the left — Bukhari 168
• Washing the head three times, and according to the majority the same applies to every other part — Bukhari
• Using a Saa of water for ghusl and a Mudd for Wudu. — Muslim 326
• After washing the body, moving from your place and then washing your feet. — Bukhari 249
• For a woman doing ghusl due to menses, applying perfume at the location of the blood. — Muslim 332

Using soap or shampoo may be recommended for better hygiene, but it is not required for a valid ghusl.

References:

• Al-Fiqh ala Al-Madhahib Al-Arbaah - (Maliki, Hanafi, Shafi'i, Hanbali) - Page 136-145
• Mukhtasar-Al-Quduri - (Hanafi)
• Umdat as-Salik - (Shafi'i) - Page 82