I should preface my response by stating that I've been vegetarian/vegan for the past three years--that is, vegetarian when I travel, vegan when I can cook for myself--so I am probably biased.
I think vegetarianism is a worthwhile thing to at least try out if you're interested in it, and 'trying it out' is exactly how I would start. Set yourself a time-period--say a week or a month--during which you will only eat vegetarian food, and see where you're at after that time-period. Even if you decide it's not for you, you'll still come way with an expanded repertoire of food you can cook!
I'm not thoroughly convinced that vegetarianism is necessarily healthier or unhealthier. However, it does force you to pay a bit more attention to what you're putting in your body, and that in itself can feasibly improve your diet. I'm not particularly advocating this site, but look for similar sites to see what you should be making sure to include in your diet. In public perception, there is perhaps bit of an over-emphasis on protein in-take (it's in a lot of standard food sources) and under-emphasis on Omega-3 and Vitamin D for vegetarian diets.
There is so much in the way of vegan/vegetarian blogs that it's hard to know where to start. I have found this blog really great as it has a lot of simple recipes. Additionally, I would definitely recommend having a go at making your own seitan. It is easy and so versatile!
One final thing to warn you about: depending on where you live, do expect that some people will get very defensive, or occasionally aggressive, about their omnivorous diet when you mention you're trying vegetarianism. This can seem disheartening, but I've found that most people don't have a problem with it once you explain why you're trying vegetarianism. That part is pretty well up to you, as you know much better than I do why you're interested in trying vegetarianism.
All the best with it, feel free to contact me if you would like any help or have any further questions!