After the takbeer and raising the hands, you should bow down into the rukoo' position, until the body is completely comfortable and relaxed in the new position. This tranquility in each position of the prayer is an essential part of prayer.

To perform rukoo' you need to bow, while placing your hands on your knees with the fingers spread out, and hold your upper arms away from your sides, as it was narrated that the Prophet (may the peace and blessings of Allah be upon him): 

"..bowed and placed his hands over his knees, while his fingers extended below them,and his upper arms held away from his sides until every limb settled in its place…"  [Abū Dāwood: 863]

Wā'il ibn Ḥujr also narrated:

"When the Prophet (may the peace and blessings of Allah be upon him) bowed, he would spread his fingers out, but when he prostrated, he would join them together." [Ibn Hibbān: 1920]

The back should be straight, to the extent that a companion of the Prophet (may the peace and blessings of Allah be upon him) described his way of bowing in the prayer:

"..he would keep back straight, as so that if water was poured on it, it would remain without spilling." [Ibn Mājah: 872]

And when the Prophet (may the peace and blessings of Allah be upon him) would bow:

"...he would grab his knee firmly with his hands then he would stretch his back forward making it straight (without any curvature)..."  [al-Bukhārī: 828]