The cheapest way is usually to buy larger bars (1 oz or bigger) from a reputable online bullion dealer rather than a local coin shop, since premiums over spot price shrink as bar size increases and online dealers have lower overhead.
Compare “price over spot” across a few dealers (APMEX, JM Bullion, Kitco are common ones), and pay by bank wire or cash rather than credit card, since card payments often carry a surcharge. Stick to well known refiners (PAMP Suisse, Valcambi, Perth Mint) to avoid resale headaches.
Avoid “collectible” or numismatic gold, since those carry much higher markups. Also factor in sales tax, which varies by state, and secure storage costs.