In the introduction to lesson 2 James mentions the student should learn both the key word and the primitive meaning of a new Kanji as they are shown. What are the best methods for remembering primitives as I encounter them?

I have done lesson 3 without making any effort to remember the primitives but I don't want to continue the book until I know exactly what I am supposed to be doing and how I am supposed to do it. Any help would be appreciated.

I simply wrote each primitive like once or twice and moved on. Heisig also writes I believe that you will learn all primitives automatically as you go on by simply using them in other kanjis, and this turned out to work fine for me. I failed some kanjis due to forgotten primitives 2-3 times in Anki first (extra rare primitives), but you quickly learn them automatically.

Thanks for clearing that up, I was a bit anxious to continue the course because of the uncertainty.

A lot of the primitives are pictographs, and as such are easy to remember. The rest show up so often that they are drilled into your head pretty much after a few reviews.

It's funny because I'm pretty new with RTK and I did not fully understand the whole primitive thing.
Until I got to about 130 kanji I was forgetting the abstract meanings of primitive (for example I only knew the kanji #13 month by moon or month, not flesh or part of the body). I ended up writing down all the primitives in order with their meanings. Occasionally I glance over the primitives to refresh my mind of the primitives and their meanings.

The concept of primitive is quite fundamental to Heisig's approach. They are the basic building blocks that you use to construct mnemonics for all the kanji.

To Heisig, a primitive is a character (and that doesn't necessary mean a kanji character) that is not composed from other characters (like "drop of", "umbrela", "mosaic"). There are some kanji that act as primitives, like 日 (sun, day), 月 (month, moon, flesh), 金 (gold, metal), 十 (ten, needle) but as with non-kanji primitives, they don't contain any other primitives and need to be remembered by heart.

When you learn a specific kanji you need to know the composing primitives first. Like in 早 (early/sunflower = sun + needle), or 朝 (morning = needle + sunflower/early + moon), for example.

Once you know the primitives, you can develop a story that glues those primitives together, so you have a consistent mnemonic for a kanji in question.