Here's some full and simple code to do this. This worked fine when I used it.
var processStartInfo = new ProcessStartInfo
{
FileName = @"C:\SomeProgram",
Arguments = "Arguments",
RedirectStandardOutput = true,
UseShellExecute = false
};
var process = Process.Start(processStartInfo);
var output = process.StandardOutput.ReadToEnd();
process.WaitForExit();
Note that this only captures standard output; it doesn't capture standard error. If you want both, use this technique for each stream.