You can open the downloaded raster files by functions raster() [open one file, get one RasterLayer] or stack() [open multiple files, get one RasterStack containing multiple layers] of the previously mentioned 'raster' package or by the function readGDAL() of the package 'rgdal'. Alternatively, you can calculate bioclimatic variables from the monthly temperature/precipitation data (RasterStack, RasterBrick, matrix or vector) by the function biovars() of package 'dismo'.
You can download and open WordClim's bioclimatic rasters in one simple step by using function getData() of package 'raster'. Alternative method: see package 'sdmpredictors'.