Among the many available methods, which are the most efficient (i.e. require the smallest sample size for defined alpha and beta) and relatively straightforward to implement?
Almost all statistical packages such as Stata, SAS, SPSS and R have the modules for power calculation and sample size estimation. For studies with longitudinal data, which is also known as repeated measures paradigm, you need a specialized package in this specific area. Freely available tools such as G-Power and PS (by Vanderbilt University's Clinical and Translational Science Award (CTSA) program ) are somewhat useful: however, PASS is the only dedicated software to encompass all power calculation/sample estimation algorithms as mentioned.
PS is Power and Sample Size Calculation Tool by William D. Dupont and Walton D. The web page http://biostat.mc.vanderbilt.edu/PowerSampleSize contains up to date information about the program.
GPower is assuming you have your data set up so that a row is a case (often a person), and a column is a measure. For example, if we measured Y on three occasions, we'd have Y1, Y2, Y3, and we'd have three measures. The groups are when you have a between case predictor - for example gender or experimental group. So when you have a 2x2 repeated measures design, you have four measures.
As a starting point you must go through this Medical research methodology paper http://www.biomedcentral.com/1471-2288/13/100.
Please also go through valuable information on page http://homepage.stat.uiowa.edu/~rlenth/Power/index.html
If you go through http://www.epibiostat.ucsf.edu/biostat/sampsize.html, you will know that only two software packages NQuery-Advisor and PASS are the one to take into account repeated nature of data, not GPower or PS.