Investing in the shares of gold mining companies is probably the best way to make a "paper" investment in gold.
The theory is that when gold bullion prices and demand increase, gold mining share prices will follow. However the theory does not always hold true - some mines "hedge" their future production. This means they contractually lock in a gold price to be paid in the future when their gold is produced, whether or not the gold price in the future is lower or higher than the contractual gold price. Consequently, if prices rise, companies wih hedged production can lose out as they have previously sold their gold below the prevailing market price. Many gold mining companies have switched to non-hedging in recent years to take advantage of the sustained bull market in gold.
Furthermore the share price of such companies is also dependent on the company's performance, world economy and overall state of the equity markets at the time. The World Gold Organisation has prevously warned that gold equities can be as much as "three to four times as volatile as the gold price."
Mining shares as a whole can be pretty risky - if in doubt take professional advice!