I've been doing research on this for a good for a good two or three weeks now, but I don't know how correct I am on this. If I'm wrong in any aspect, whoever has an in-depth knowledge in this please correct me.
I'm going to break this part up into a few sections a little so it's easier to understand, and I will only cover the things I feel are the key differences.
Keyword Research:
National: Nothing special here, just standard stuff. As an example, let's just say "how to do yoga at home" or something like that.
Local: I think the difference here is that for keyword research, it's just tied to a geographical region. For example, it would be like "best yoga places in NYC". The difference here is that to use a keyword like this, your actual place of business requires an address located in NYC in order to be ranked on the first page. Other than that, I don't see any significant differences in keyword research.
On-Site Optimization:
National: Once again, just normal stuff that you should probably already know or could do a quick search on. I actually don't 100% remember what everything is since I got so used to just outsourcing this, but I believe it's just things like meta descriptions, meta tags, <h> tags, and probably a few other things I totally can't remember off the top of my head. Sorry, but I totally suck with this.
Local: Same stuff, but I think the key difference is that you need a business address listed as well on your page. I couldn't really find a huge difference in terms of on-site for the site itself. However, as an example for the next part, let's say your address is "123 ABC St"
Ranking:
National: Once again, I can't really explain it that well, just your regular stuff. (I suck, I know)
Loca: Seems to me, the largest difference is using properly optimized Google+ listings, a good amount of reviews on Google+ (5 reviews to get the stars to show), and using properly optimized local citations. One of the things that is most important I find everywhere, is that the business address must be the same across all the citations and listings and wherever else. Like I used above "123 ABC St" must be used across everything, using something like "123 ABC Street" instead and mixing it up would totally screw you sideways.
I know my explanation isn't very descriptive, but there's not a HUGE difference between the two. At the very core, it's the same thing, you just have a slightly different approach is all.
Also, to apologize for my really shitty explanation, here's a few really useful links I found for local optimization:
http://www.shopify.com/blog/1515607...on-tips-for-local-seo-to-help-you-rank-higher
http://www.poweredbysearch.com/skyrocket-local-seo-google-plus-local/
And finally, something like a huge directory of everything:
http://radicalmustache.com/ultimate-local-seo-guide/#ch2
Anyway, I hope I helped you out at least a little bit or pointed you in the right direction.