taking away
times tables
Practising Arithmetic

For the early years, we need to remind ourselves about the five principles of number (see Number and Counting) that are:
one to one principle - to do with counting
stable order principle - when counting it is always in the same order
cardinal principle - how many of something doesn't require counting
abstract principle - how many of something doesn't matter about properties like colour or size
order-irrelevance principle - a quantity of something doesn't depend on how they are laid out

these are all learned skills for the early years,
the important one for adding is:
the cardinal principle
it is important for progression that children can count on rather than always have to begin from the start - there are too many still using their fingers and counting from the first finger to add

It is also important that they realise that the order is irrelevant, 
1 + 2 is the same as 2 + 1 (the commutative law of addition)

so with these things in mind, there are a number of techniques to consider and practice:

put two groups of items together and count them up
put a number of items on to the current total (cardinal) and count on
using fingers to count up

early learners need to get to working with numbers and the plus sign

1 + 1 =          is an example
or getting them to understand that the sum could be put vertically (chimney sum)
   + 1
                                 chimney sums makes it easier to add larger numbers

and here are some interactive examples

they could also be introduced to numbers on the 'number line' and jumping to the right from the cardinal position on the line the number of items to add on.

For worksheets, try here.