Judging from your question you want SC2 over LAN without connecting via the Internet. There is no easy way to do this. As McKay points out, as long as all computers are connected to the Internet you can use computers which happen to be connected to the same LAN, but make no mistake you will not be leveraging the advantage of said LAN.

Now I said "easy way," because there is a "hard way." Blizzard does have a LAN client of Starcraft II which is provides for reputable tournaments. Gaining access to this requires setting yourself up as a business organization and paying a licensing fee. For more information you're going to have to contact Blizzard directly.

That said, for a couple of friends, there is no legal way to leverage your LAN for SC2 games without going through Blizzard.

Using the numbers tzenes gave:

• Start out with 8 mineral patches, each with 1500 minerals
• Start with 6 SCVs (right?)
• An SCV takes 22 seconds to build
• The first 2 SCVs on a mineral patch will gather 45 minerals a minute each, while the last one can be considered to gather about 12

In other words, there are 12,000 total minerals to gather; the first 16 SCVs will gather 45/min, the last 8 will gather 12/min. Using this knowledge (and not taking MULEs into consideration!), we can construct a table:

 Seconds  | Number   |  Resource gather rate  |   Total minerals
 elapsed  | of SCVS  |  (minerals / minute)   |  gathered (approx)
------------------------------------------------------------------
        0 |     6    |          270           |        0
       22 |     7    |          315           |       99
       44 |     8    |          360           |      214.5
       66 |     9    |          405           |      346.5
      ... |   ...    |          ...           |      ...
      198 |    15    |          675           |     1485
      220 |    16    |          720           |     1732.5
      242 |    17    |          732           |     1996.5
      ... |   ...    |          ...           |      ...
      374 |    23    |          804           |     3672.9
      396 |    24    |          816           |     3967.7

So at the time your 24th SCV is built and you become fully saturated, you could have mined about 3968 minerals. The remaining 8032 will then be mined in about 590 seconds, giving an overall time of 986 seconds, or about 16 and a half minutes.

Of course, this is a lower bound. In a real game, the actual time will be slightly longer because:

• Some SCVs will be building/scouting
• Some SCVs will be mining gas instead
• Not all mineral patches will deplete at the same time, so your resource gather rate will actually go down near the end. Hopefully by this point, you have several other expansions :)