You might consider trying a service rifle match, such as they have out at Douglas Ridge. I've shot 2 so far and learned a lot about shooting at distance with open sights. My eyes aren't horrible, but they're getting worse as time passes. So, I tend to shoot with glasses.
One thing I learned is that you shouldn't be focusing on the target, rather, you focus on the front sight. If you're not used to doing this, it will take some practice. The target will be blurry, but you can make out the black center of the target - and you simply dot the 'i' as someone else noted above, over the front sight.
In a service rifle match, as distance increases, the size of the target increases, so your sight picture is the same, regardless of distance. My first match, I did a fixed 100 yards. The second match, we did 200, 300 and 600 yards. For a first timer, you take a class the night before the match. They teach you about sight picture, how to adjust your sights for distance and how to score your targets. At DRRC, they have club M1 Garands you can rent for the match - in the class, they'll also teach you how to shoot the Garand.
As @Joe13 recommended, Appleseed would be a good choice too. I'm planning to do one one of these days myself.
One more plug for the service rifle match - if you're new to it, you can count on some experienced folks to give you some great tips and help along the way. No pressure, just learning new techniques.
etrain, has it absolutely right about only focusing on the sights and not the bullseye. I should have mentioned that little item in my post too.
When we're young we can often focus on all three, at least to a certain range! Aging eyes lose all ability to focus on sights and a target at any distance! As I taught my kid and grand kids "focus on the sights, put them on the base of the blur."