Most students are developmentally ready to begin two-digit addition with regrouping in first or second grade. By this point, they can rote count high enough, and have some understanding of quantity. They also understand that the sum will be larger than the two addends, an element of number sense. This will allow them to determine whether their answer makes sense.
To master two-digit addition with regrouping, students need to understand place value, that a 7 in the tens place means 70, and a 7 in the ones place means 7. This can be strengthened with activities using manipulative materials, in which students bundle groups of 10 objects and write the numbers created. One helpful game is Race to 100, in which students roll dice to collect that number of Unifix cubes. When students have 10 single cubes, they group them into a stick of 10 and move them to the tens place.
When students can regroup objects and name the two-digit quantities in numerals and words, they are ready to begin adding two-digit numbers with regrouping. Begin with the same manipulative materials and have students begin to physically combine two-digit quantities. When students have practiced regrouping physical objects, begin to teach the algorithm. Continue to use objects to model the problems, and connect them to the algorithm by using questions like "What do we do when we have more than 10 ones?" Students will gradually need less support with objects as they internalize the process of regrouping.
Many students will struggle with part or all of this skill. Some will make errors such as ignoring the regrouped 10 when they add the numbers in the tens place. Return to objects with these students to explain that they can't ignore the regrouped 10. Others might line up the numbers incorrectly, ignoring the place value of the digits. Give these students a template labeled with hundreds, tens, ones, with dotted lines in between, to help them organize their work. Continued practice will make a significant difference in students comfort and success with addition.