An analog modem cannot be used on a leased line - you need a DSU/CSU at each end. If the range isn't far, you can use a long-haul modem (Black Box makes one). Either solution will be slow and less than convenient. If you are very close (within 100 M) you can install NICs in each machine and use an Ethernet crossover cable.
I've been fighting this battle for two years, as a 2-pair copper line is the best our telco has to offer. I think I must have read the same articles you have, as I wasunder the impression it would be easy. Then I found no option in WinNT to network via a serial line to a DSU/CSU. Since our locations are 6 miles apart, a direct serial connection won't cut it. I finally went wireless - it cost a bit up front, but quickly pays for itself, as the leased line costs $100/ month! Check out the Lucent Orinoco products at www.lucent.com for examples of wireless offerrings. CDW sells their products, so you can get an idea of the costs from their online catalog.
Good Luck!