How do I apply this operation to a list?

Outer[Append, mylist, mysecondlist, 1]

{{{a, b, 1}, {a, b, 2}}, {{c, d, 1}, {c, d, 2}}}

Also

Outer[Join, mylist, List /@ mysecondlist, 1]

Flatten /@ Tuples[{{#},  mysecondlist}] & /@ mylist

Flatten /@ Thread[{#, mysecondlist}, List, {2}] & /@ mylist 

Distribute[{mylist, mysecondlist}, List, List, Partition[{##}, 2] &, Append]

all give

 {{{a, b, 1}, {a, b, 2}}, {{c, d, 1}, {c, d, 2}}}

My train of thought to tackle that problem would be the following:

Each of the elements of your desired solution has the elements of the second list appended.

I would first try to construct each element separately. The first element would be.

Append[{a, b}, #] & /@ mysecondlist

which gives

{{a, b, 1}, {a, b, 2}}

Afterwards I would replace {a,b} by a variable and use Map to obtain a list of all elements.

Function[{x}, Append[x, #] & /@ mysecondlist] /@ mylist

which gives

{{{a, b, 1}, {a, b, 2}}, {{c, d, 1}, {c, d, 2}}}

So in short: Try to divide the problem in smaller, easier solvable chunks.