Freestyle guitar soloing is what the name implies; freestyle soloing involves playing a guitar solo without intentionally adhering to any pre-determined style or specific musical scale or key. Freestyle playing is simply another form of improvisation, with the guitar player making it up as he goes. The primary difference between freestyle playing and improvisation is that the guitar player plays alone.
Begin with a pattern. Although freestyle affords you the freedom to do anything you want, a simple pattern can get you started. Freestyle solos are built by stringing together a series of patterns that repeat. Begin with something simple. Play three notes per string, with one open fret between each of the notes.
Play your pattern forward and reverse, starting off slowly and building speed gradually, with each pass of the pattern. Allow yourself to add techniques as they come to your mind, but don't think ahead. As soon as a technique comes to mind, put it into play. This can include bending strings, hitting a tremolo bar or changing the rhythm of the notes you're playing.
Move your pattern up the neck (higher in register). Add an additional note per string and use your fourth finger to play the note. Add some color to your solo by playing two strings simultaneously, dragging your pick along the strings between patterns or by filling in between solo runs with a chord or two.
Experiment and don't limit yourself to specific techniques. Your freestyle guitar solo should come from a collection of playing techniques you've learned over time and be created on the spot, without planning.