Access Matrix field that is assigned to a user
You need to use 'currentUser' to access the field. So;

{% for block in currentUser.myMatrix %}
  {{ block.myMatrixField1 }}
  {{ block.myMatrixField2 }}
{% endfor %}


As for creating a new record in the matrix (I'm guessing you mean from the front end) then you need to create a form that submits the current matrix data alongside your new block data. This isn't super straight forward, but basically you need to create a user profile form that submits the current matrix data alongside the new data.