If the piece were truly random, you would assemble all your desired material and just pop it onto your base with reckless abandon. You would pluck out each part, and wherever it lands, it lands. Que sera, sera. You get the idea. But the result would probably look more like a gift from a child than an art piece. Why is there a big chunk of orange right there? I can't stop looking at this clump here. Those two parts look hideous together! My eyes just want to look away!
You find that what you are really looking for in a 'random' collage is the illusion of chaos. Something which holds so many curiosities the viewer is compelled to admire it for an extended moment, just to unlock all the hidden treasures within. Something which remains just as lovely from afar.
To achieve this, painstaking effort is made to ensure that every piece complements its neighbors as well as flows with the whole. Colors & materials must be chosen with careful consideration to how the eye will perceive them both individually and together. What shade is this? Does it brighten or dull the others? Is it a stage stealer? Does it sparkle (reflect light) or is it dull (absorbs light)?
Like selecting the perfect cast for your favorite play--you myust hire actors who are brilliant but are also all working to bring the superbly-written play to the audience. If one is too loud, competes with the others, is just slightly out of place, or decides to take the play in a different direction--the audience will never forget they are watching people pretend to be characters in a play. As the "director" of your collage piece, you alone decide will stand where and by whom. You must look at the micro-scale and the macro to understand how others will view it from various depths.
Important things to consider for a "random" arrangement:
Color- The color wheel, a grade school basic, can be instrumental in showing you how humans will see the colors in your piece. The lessons from it are numerous, and should be another topic, but for now, consider how the colors you've chosen might solidify a cohesive piece or make it visually jarring. Some tried and true pallets could be monochromatic (many shades of one color) or complementary (color pairs from across the wheel that are known to look harmonious, like blue and orange, red and green, and yellow and violet). You could have a range of muted colors of the same hue or a rainbow of brights, held consistent by their shared tonal value. If there is too little consistency, the eye will be frazzled by the juxtaposition, and want to look away.
Material- shiny, dull, sparkly, frosted, iridescent, metallic, opaque, semi-opaque, tinted, lightweight or heavy, there are infinite different types of materials you might be using. As a strategic accent, materials of different finishes may benefit your arrangement, while overdoing it might have the opposite effect.
Size- likely the easiest to control, different shapes and sizes can evoke a sense of movement, and dictate where attention will be drawn.
The most important concept to embody in a "random" piece, however, is balance. Choose which feature is most important to display and base your arrangement around that. For instance, if you have many different textures, or of different shapes and sizes, consider limiting your color palette to monochrome or a complimentary duo. By narrowing your range of color, you keep the whole piece cohesive while going wild with other features.
Conversely, if color is paramount, select a narrow spray of materials. Want a mix of the shades of your favorite summer garden? Choose several pretty hues and keep your materials relatively consistent. The point is, choose something, not everything, to randomize.
Be prepared to arrange your materials many times before you decide on the perfect combo. Place, replace, move, swap, shift... balance. Look at how individual items look next to each other and how the whole piece looks from afar. Is your eye drawn across? Vertically? Does it stop anywhere and fail to move on? Does it make you look away? Does one "chunk" seem too different from the rest? Does it hang symmetrically?
When all else fails, leave it alone for the night and look at it tomorrow. Do you still love it? If so, snap a photo (I use my cell phone) so you have a reference at hand while you're putting it all together.
Whew! Never knew "lacking order" was so...orderly!