Children Developing Self-Worth - a Personal Observation

In the last few weeks, I have had the opportunity to spend time with my youngest grandchildren, ages 10 months to 4 years in age.  I have enjoyed interacting with them, but I have also appreciated the opportunity to observe them as they played, investigated, and problem-solved in their wonderful world of inquiry.  I noticed how the older ones have learned to navigate safely in their environment including steps, sofas, chairs, beds, uneven land, and other things.  The 10 month old is fearlessly learning those things as she anxiously presses forward in broadening her skills.
As I watched them, I was aware of the look of satisfaction and accomplishment their little faces showed when they were successful.  An experience with the 10 month old was particularly insightful.  She loves to put blankets in front of her eyes and over her head and then peek out.  One day she had a larger fleece throw.  She was doing the same as always, until her hands moved toward the center of the cover.  She would move the cover almost to the edge and then pull the other way.  I watched as she worked at it.  Since I didn't want her to become frightened, after numerous tries I helped a little but in a way she didn't realized.  She pulled the cover off and I said the traditional "peek" several times, then I noticed how proud she was.  Her little face beamed.  I clapped, she clapped, and we celebrated her success.  The real reward I experienced was seeing her so happy and proud of herself as she was successful and to see her self-worth grow.  The thought reinforced itself that afternoon that we are instrumental in the development of children's self-worth.  How we interact with them as they learn, problem-solve, and investigate the world in which they live makes a difference in how they see themselves.  
How can we do that?