OK, first a basic explanation: LR is not like Paintshop or Photoshop because it is a Raw converter and all Raw converters work non-destructively. This means that any edits that you set in the Develop panel are not actually carried out on the original image file, but rather only recorded for future reference. That future moment comes when you export (create and output) a new tif, psd or jpg file, send an image to Photoshop or some other secondary editor, or send the image to a printer.
Now for the cropping: Select the crop tool in the tool bar under the Develop histogram. A drop-down menu offers a selection of the more common aspect ratios or you can set a custom ratio. Use the X key to toggle between landscape and portrait orientations. Set the crop box to the size and location you want by dragging the corners and close it. The crop is recorded in the catalog database file and this info will be used when you export the image. Because no actual cropping and/or resizing is done until export, the resizing instructions are on the Export dialog. This way the same crop configuration can be used with differently resized exports. Tick the Resize box and put in the pixel dimensions you want. Alternately, put in a size in inches or centimeters and a pixels per inch (ppi) resolution and LR will calculate the pixel dimensions. If you are resizing, I'd highly recommend also enabling Output Sharpening. It is interactive with the resizing and automatically does the optimum sharpening for the amount (and type) of resampling being done.
If you want a number of images to be the same size, export them all together by, after editing and cropping them, selecting them all in the Library grid or the filmstrip and then running the Export dialog