I have been teaching my 8 and ten year old daughters how to ride over the past few weeks and with my 10 year old daughter, who was the most nervous, I stressed that she needed to stay relaxed and release her death grip on the handlebars.
A bicycle wheel is a gyroscope and is the least stable when it is at rest and once it is turning it will resist being turned to some degree... if the rider and bike are well balanced , it should move in a straight line as long as there is no rider input.
Redirecting the bicycle involves push steering and leaning the bike into the turn to maintain one's position on the bike...it is only at very low speeds that one would turn the bars to steer the bike and when the bike is at this lowest speed that it is the most unstable.
It is actually easier to ride a bike at a slightly higher speed due to the gyroscopic forces generated by the front wheel which keeps it going straight... once my daughter learned this she was quickly riding solo and now rides with a great deal of confidence.
Know that at first you will find yourself riding towards whatever you are looking at so avoid looking at the road immediately in front of you, keep your head up, and look to where you are going.
Having a stable / upright bicycle will make learning to ride a great deal easier... it takes some time to learn how to handle a road bike and if you ride a mountain bike, you may want to raise the bars (if you can) or install a riser stem to bring the handlebars higher.
I also raised the bars on my 10 year old daughter's bike so she could have a higher hand position which also causes her to keep her head higher and look down the road instead of right in front of the bike.
My 8 year old daughter's bike is a bmx style and already has a high bar / grip position and she is an animal on a bike after only 2 weeks of solo riding... she practises her riding every day even if it is raining and this too is important.