The percentage of films produced compared with the number of screenplays written is extremely small and, as is the case in many industries, success can largely be based on having the right connections. Universal Studios, or any major studio, is not simply a singular entity--production companies exist within and independent of the studio that actually make the films. The studios distribute and market them. Films greenlit and produced directly by the top executives at Universal are most likely the big-budget major releases, made by people already proven in the business. For the best shot at getting a deal at Universal, have a great script in hand and work with an agency that can get the deal done.
One of the cornerstones of getting a movie made is having a great script. Use industry-recognized screenwriting software such as Final Draft, which properly formats the script and makes it easily transferable to other formats. When completed, get educated, unbiased opinions on it and re-write when necessary. For those without an agent or solid industry contacts, entering the script in respected screenwriting contests can be a good way to get noticed by an agency and/or studio, which can pave the way to getting a deal done.
For new writers, finding an agency to represent them and present their script to the studios is not an easy task. The long-standing Hollywood Catch-22 is that you can't get a deal without an agent, but you can't get an agent unless you have a deal pending. Find an agency that is looking to represent new writers and that will accept unsolicited screenplays. Different online sites, including the Writers Guild of America, list current contacts for literary agencies and their policies concerning new writers. If the script is good enough and marketable, the writer has a chance of getting signed and having someone to present it to studios.
With or without an agency, another route to getting a movie made is to get an established actor to look at it and agree to do it. Again, this is much more likely from someone already in the business; an agent will have a much better chance to get an actor or studio interested than a civilian. The more commercial a script is and the lower the potential budget, the better it looks to a studio. If the goal is to get it produced at Universal, the agent can take it directly to the studio, or to one of the production companies that works with the studio. If a deal gets done, these companies will have the ability to line up the cast, crew and facilities to get the picture made.