For raw sequence data like WGS (whole-genome), WXS (whole-exome), RNA-seq, and miRNA-seq, you'll need to query CGHub, add the files to the cart, and download a manifest XML that can be used later with the CGHub downloader. You'll also need an access key, for which you need to request authorization, or you need to find someone in your group that already has it.

This data matrix that dcolinmorgan mentioned points you to most TCGA data levels/types, but raw sequence data is handled by CGHub because of the enormity. You can read more about TCGA data levels/types and their availability over here.

It seems to be down for maintenance right now. However, you can normally use the data matrix/grid to select studies (horizontally) and type of data (vertically) of interest, ie miRNA, RPPA protein, clinical. This is the visual means for pulling such individual sample data, however, there might be a backend method I am not aware of. I will check back when the site comes back online, around 1pm EST

You can download data from TCGA File Search Option. Input the barcodes in the Barcode/UUID Field, each barcode separated by a comma. But I doubt you will get WGS data on TCGA. However, you can get mRNA/miRNA expression, DNA mutation/methylation/copy number variation, Protein expression data.