I'm not saying it's easy but it's not impossible to eat healthy on a budget. Eating healthy should not be a hardship but often times it can be if you don't know the basics. Below are just a few ideas I put together to help you get started.
1. Buy fruits and vegetables that are in season. They will not only cost less, because they don't have to be shipped, but they will also taste better. If you can't buy them fresh frozen is a great option. But be sure you are getting just veggies and not added sugar or salt. (read packages carefully)

2. Grow your own. This may not be practical for everything, but even just growing the few herbs you use most can save you money. And since you've grown it yourself you know that it has't been treated with any harmful chemicals.
3. Cut out processed food. The sugar and salt they contain will only leave you hungry for real food; which means you end up eating more. You may need to "condition" your taste buds for this one but once you do it becomes routine and easy.
4. Use leftovers wisely. One meal can often be spread out into several others during the week. Leftover chicken from tonight's dinner can be tossed in a salad for tomorrow's lunch. Veggies can be sauteed and added to eggs to make a nice hearty omelet.
5. Prioritize. What's important to you when it comes to food? Most people have no qualms spending upwards of $5 at Starbucks on a daily basis but think it's outrageous to spend that much on fresh veggies. If you decide that you want to eat healthy then spending a little extra for good food will become less of an issue for you.