I don't know there is a wrong way as long as the water is up to temperature. Some turtles are shy at first and acclimate. Other turtles like mine will explore right away.
You may want to place your turtle on the basking area and let them go from there.
I put mine on the basking area and let her go in on her own. It's how i always put her in there, even after feeding her. Not sure if i'd like to just be plopped down into water without any warning lol.
If I ever put her on her basking area she will zoom like mad into the water. Even once when she couldn't get up the ramp I gave her a hand. No she wants to get up there on her own accord.
Just place her in the water slowly supporting her from underneath. Let her swim off herself. THis way she will become accustomed to your hand and it is kind of cool when my turtle just stays on my hand.
I have two female red ear sliders. Chimpy - 5.5 inches Chompy- 6.0 inches Both were born about 7/2007 Got them -- 9/2007