There are two real GDP per capita variables: RGDPL and RGDPCH. Summers and Heston (1991, page 344) recommend using the RGDPCH.
It's rather difficult to understand how the widely-used Penn World Table calculates real GDP per capita in international dollars. So here's the rough summary. For more detailed accounts, see Johnson et al. (2009).
1. Collect data of prices of hundreds of identically specified goods and services prevailing in each "benchmark" country (this is done by the United Nations International Comparison Program, or ICP).
The PWT version 6 uses the 1993 ICP data. As the 2005 ICP data is now released, GDP figures in international dollars are likely to change. See Arvind Subramanian's article on Dani Rodrik's blog.
2. Obtain PPPs for the benchmark countries by comparing the prices of each good and service.
3. Use capital city price surveys by United Nations International City Service Commission, Employment Conditions Abroad (a British firm), and the US State Department, to estimate PPPs for a wider range of countries.
4. By regressing PPPs obtained in step 2 on PPPs obtained in step 3 for the sample of benchmark countries, PPPs for non-benchmark countries are estimated based on their PPP estimates obtained in step 3.
5. Use PPPs to convert the countries' national currency expenditures (from national accounts) to a common currency unit.
Steps 1-5 were carried out for the base year (1985 for PWT version 5; 1996 for PWT version 6.1).
6. Real GDP per capita in PPP for other years is obtained by applying the growth rates from the constant-price national accounts series to the base-year real GDP per capita.
See pages 329, 341-4 of Robert Summers and Alan Heston (1991) "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988" Quarterly Journal of Economics, 106, pp.327-368.