You don't feel like paying a lot of money for the services of an SEO consultant or for one of the automated tools/plugins that would do the work for you? Well, you can do some of the things yourself, things that are easy to do but will make your blog a lot more discoverable.
1. Pick a proper niche
Make sure the blog you're working on belong to a specific niche. This can be anything you can think of - health, fitness, SEO, drinking, PC games, board games, photography - anything, as long as you are constantly aware of the fact that this is what you will be writing about and this is the kind of content that will be posted on your site.
2. Pick a good looking site design
While the basic site templates for all of the popular blogging platforms can certainly work, it's not google crawlers that do all the work, at one point or another a live person will come and take a look at your site and grade it as far as search engine rankings go, and that person needs to be impressed with what it sees. A high quality visual theme like Connect can make your site stand out from the crowd.
Don't go overboard with this either. Too many flash and java elements can confuse the nice robots looking through your site and prevent parts of content from being discoverable, something you want to avoid at all costs.
3. Provide a clean site map
There's a golden rule to making your site SEO compatible - don't confuse the nice robots. Provide them with a clean and nice looking sitemap and try to cut down on all of the fancy code work - they like original and exclusive material sorted in a clean manner. Sure, there are things like redirect codes to point the web crawlers in the right direction, but time has shown that all of the gimmicky code just doesn't live up to the clean file and content structure.
4. Provide content of high value
Original, exclusive, well written, easy to understand and high value content is what will get you good ratings. Also, there's a big misconception that a blog post should not have more than two or three links. This is simply not true. Sure, Google reduces the value of linking for each link on the page present, but you gain much more if the links are meaningful, in context and leading to other good quality content than you lose on the number of links. This is a mistake most beginners, and even some who consider themselves SEO experts make. Remember, the Internet is about sharing information, and sites that lead to other sites are often the most popular ones. Don't believe me? Reddit, Digg, StumbleUpon - all of these services lead to other sites and yet the page visits they get on their site are very high.
The text should be the main communication form on your blog, as that is what robots can read and try to understand the easiest, but the presence of pictures and even videos is encouraged, as long as it's used in moderation.
5. Use a free SEO tool for each of the posts
Free SEO tools allow you to things that can make your pages much easily discoverable. Add a SEO Title tag, define what's the main keyword, add a meta tag for search engines, add 3-4 tags for each of your posts, add a featured image, add author (preferably a Google+ profile author, as I'm sure Google is pushing towards this method of authenticating validity of posted content) and your page has a lot more chances of being found. Don't bother yourself too much with keyword density, keyword tails and similar advanced SEO methods - unless you really want to get into the SEO business, but that takes a lot of research a casual blogger just can't dedicate himself to.
6. Add social sharing buttons
Clean and neat social sharing buttons on your blog can do a lot for you, especially if you get some decent initial traffic towards your post and if the post itself has value. These will allow people to share your content more easily, getting you traffic from their friends as well.
Neither of these techniques should take you more than 5 minutes per post, and most will take a lot less of your time, but they can all do a lot for your search page rankings and ratings, so they're worth spending time on, too.