The budget solution is to calculate relative positions from a corner stake.
You will need a compass, a clinometer, a tape measure, a notebook, and an assistant. Starting at the known location, take readings for azimuth, inclination, and distance from the base point to your point of interest. If the point of interest is distant or around obstacles, you can make a chain of survey points. In the series, take measurements from point A->B, B->C, C->D, etc., until you reach your destination. You can use simple trigonometry to determine the relative positions.
To maximize accuracy, take readings as close to the survey stations as possible and record readings both from A->B and B->A. Good equipment helps too; for such tasks, I use a SUUNTO KB14 compass and SUUNTO PM5 clinometer. A Brunton Pocket Transit would work for your accuracy requirement, and can sometimes be found at military surplus stores for cheap. A laser measurer, plumb bob/protractor, and hand compass might work too (note: I've never tried that particular configuration. Making a loop from a known location to point of interest and back to the known point, and then assessing the closure error can provide a helpful metric of accuracy).
Relative position calculation functionality and error assessment are common in cave surveying software. See for instance, Fountainware's COMPASS Cave Surveying software (shareware). Such software often has GIS data export too.
For more pointers, you might check out web resources on orienteering, cave mapping, or land survey. Getting precise positioning requires practice, training, and skill. However, for 1' (0.3m) accuracy in distances likely within a 2 acre (~8000m^2) area, a careful novice could get satisfactory results.