I'm sure there will be some guys who come on here with much better advice than this but it's worked for me before.
Take some string and attach it to the outside of each foul pole. Run it all the way to the backstop and where the two lines cross. That is where the point of homeplate will be. With these lines still down measure out 90' for first and third bases. Now you will have homeplate, corner bases and foul pole all in a line.
Then you can take another piece of string and run it from the tip 60' 6" and that is where the pitching rubber should be. Just be sure that it is square with home plate. We did it by running more string from the edges of homeplate to the mound. The plate is actually wider than the plate so don't let that throw you. Once you have the midpoint and equal distance on each side of the string you should be square.
Then with first and third in place take string and run it up against the edge of the inside of each base. Where the strings cross is where you put second.
Now you should be good to go. I played at a community park as well and had to do all kinds of repair / maintenance work myself. We didn't have access to all the equipment to actually do the work easily so this is what we came up with.
If we were off it wasn't by much because we measured again once we had everything laid and it came out to the distance it was supposed to be and our foul lines were always straight.
It's a lot of work but not that bad.