What is happening in the following examples taken from children's speech?

• I runned
• two mouses
• my foots
• he feeled shy
• he satted on the truck
• he drived himself.

The child is attempting to use plurals but not in the correct way. However, a sense of good logic is definitly present in what they are trying to say - (foots sounds more plausible that footses for example) They don't yet know that iregular pasts usually involve changing the middle letters rather than adding something on the end. (Eg. Mouse and mice rather than mouses.)

B.F. Skinner

                             B.F Skinner and the 
                     Language Acquisition theory

Skinner's theory of behaviorism links to his ideas on language. Basically, humans learn the differences between right and wrong through experience. And that experience involves either 'pleasure' or 'pain'. For example if you steal from a shop and get caught, the negative procedures that you would go through will most likely want to make you never do it again. And likewise if you give money to a homeless person, they are likely to thank you and you are likely to feel good about yourself. Well this is how Skinner's theory of language acquisition works. 
When a child is babbling and producing noises and 'words' that don't mean anything and eventually when the child produces a sound that sounds similar to a real word, for example:
'bah' when they mean 'ball', the parents would praise and encourage the child and say something like 'yes, that's a ball! Can you say ball?' with much emphasis on the word they want their chil to say. Over time, the child will learn that good things happen when they say what their parents encourage them to say. And soon enough they will be able to say the entire word.

Many people, however, have criticized Skinner for this theory because of its reductionist approach. In other words, many people believe that this theory is far too simple and fails to explain the complex working of the human body and brain.
On the upper hand, this approach is very easy to understand. Personally I think that Skinner's theory is very plausible, albeit simplistic. But then perhaps Skinner has grasped the most basic part of how humans acquire language, but there is more hiding away waiting to be discovered?

Response to Piaget's theory on linguistic development

Jean Piaget Himself

Piaget talks about how small babies communicate primarily through basic physical actions - they're figuring out how to move around which eventually leads to crawling and walking. 
- " In the process she learns how to imitate some of the sounds she hears her parents making and in what context those sounds should be made." - Although the child cannot yet say specific words, she understands (to an extent) the nature of the intonation of certain words and when they should be made. For example: 
Mum: "Are you hungry?" There is a lot of emphasis on the question to help baby understand and encourage a response. The baby would probably respond with a high-pitched joyous sound as if to say 'yes please!'. 
Piaget's theory supports this because of her ideas on basic understandings of context and when may be appropriate to do certain things.

After the Sensorimotor stage, at discussed above, the child moves on to the Preoperational stage. According to Piaget this begins at 2 years and lasts until 6 or 7 years of age.
- " The defining feature of this stage, in Piaget's view, is egocentricity. The child seems to talk constantly, but much of what he says does not need to be said out loud." - It is evident that labeling words are the most commonly used by young children as it's essential when getting a grasp on the very basics of language.

The Concrete Operational Stage begins at the age of 7

An interesting TED talk on child's language development - worth a watch. 

http://www.ted.com/talks/patricia_kuhl_the_linguistic_genius_of_babies.html