It is very difficult to accomplish this nowadays with the "banner syndrome" (failing to notice advertisements in publications) sweeping the globe thanks to shortened attention spans, but do not let this discourage you. The subconscious mind is a very powerful thing, and if you were to target the right audience and they skim through an ad or business card, they will be very tempted to look at the ad if you:
A) Make it noticeable or eye catching
B) Ensure that the ad promotes something on that blog that you feel they absolutely -need-, even if you have to convince them of it in the advertisement itself
One technique I find that works incredibly well is securing an advertisement in a newspaper. Call up your local newspapers or read through them to see how they format their ads. If you're lucky, you will find sections like finance or sports where you can easily promote your blog if it falls into the niche. If not, then you can try regular ad placements as well as custom spots if you convince them with the right price within your budget.
This works better than handing out business cards or driving around all day with a car ad because, most of the time, people are already in their homes when they read the newspaper. In fact, many consumers these days have their smartphones right there attached to them wherever they go, so if a new mother was interested in the information on your site after seeing your ad, it will be much easier for them to type out the full blog address instead of waiting until they get home or something and forget it altogether. This is also why it pays to have a shorter domain name since it is easier to remember, but it should not be too much of an issue in the newspaper. Good luck!