Create a new Graphic and populate the Graphic.Attributes dictionary with the values, then add the graphic to your featurelayer. If AutoSave = true on you feature layer the graphic will be pushed back to your table. If AutoSave = false on your feature layer you will have to call FeatureLayer.SaveEdits()
Example:
Say your table has two fields, FirstName (text) and Age(integer).
your graphic would look like this.
Graphic graphic = new Graphic()
graphic.Attributes.Add("FirstName","John");
graphic.Attributes.Add("Age", 25);
MyFeatureLayer.Graphics.Add(graphic)
MyFeatureLayer.SaveEdits() // <-- only need if MyFeatureLayer.AutoSave = false;