Very common for 20-60 nucleotides, but can be done for 3000 nucleotides.

You can make them via chemical synthesis.

There are four nucleotides that make up DNA (A, T, C, G). If you want to make a sequence such as ATGCCGA, you start with A, react it with a bunch of T and wash, react it with a bunch of G and wash, etc to make your sequence.

To avoid uncontrolled polymerization, you use nucleotides that are capped, so they can only react once. This requires an intermediate step to activate them for reaction. So you start with A, decap it, add a capped T, wash. Then you decap, add your capped G, wash, decap. This let's you control exactly what your final sequence looks like.