The adaptive lasso was introduced by Zou (2006, JASA) for linear regression and by Zhang and Lu (2007, Biometrika) for proportional hazards regression (R code from these latter authors).
For linear regression, we provide a simple R program that uses the lars package after reweighting the X matrix. We choose the tuning parameter using the "known variance" version of BIC with full model MSE for estimating the error variance. Example call and output and plot of BIC versus model size. This "known variance" version of BIC seemed to work well in simulations and matches up with the software below.