Sigh. Okay, I'll give advice that's accurate since the wiki articles are still out of date for strategy in many cases and I haven't done anything about some of it so I can't complain too much ^_^.
The fastest way to westernize right now requires only quest for the new world. Get fleet rights, explore to Brazil + Caribbean, and have enough ADM so you can buy back 2 stab after no-CB on Portugal. Anyway, when they have a colony at 900-950 population, no-CB them, seize it, and peace out. You'll have to give them money and war reparations but oh well.
It's recommended to have DIP 3 or exploration ideas 4 so the colony will actually finish in a timely fashion. When it does, you have a core. As long as this is adjacent to a western core, you can westernize. My record in 1.7 was 1511.
Now, some speculation is that such will be changed or nerfed. I'd rather see the westernization requirements simply be reworked so that there's no true incentive to seize colony to westernize, and historically PI has instead come up with solutions that frustrate me, but 1.8 has some really good stuff so we'll see if they leave it, nerf it oddly, or change things up. If that comes to pass, there are a few other methods available as well, that can get you there much more quickly than bothering with DIP 7.
Besides, you can colonize Alaska at DIP 3 from Siberia now, all you need is 240 range from tech + exploration 3. If you want to go that route, just vassal someone in Mexico early so you can diploannex them when you get a colony in range. If you can also annex a minor on the coast to chain down there faster, so much the better because it will save you colony time.
