hand applique is usually needle turn applique- you use freezer paper templates to cut out your shapes- making them a little larger for a turn under allowance-and hand stitch them- there are tons of tutorials to teach you this technique- just search 'needle turn applique'
machine applique is often done using a fusable product- the pattern has to be reversed- drawn/traced onto the paper side of the fusable- fused to back of fabric- shapes cut out on the lines=then fused onto background. it is also called raw edge applique- because the edges are not turned under. after fusing you machine stitch the pieces-this can be done with a small zig-zag- a straight stitch- or a machine blanket stitch.
fusables are not generally used for hand applique because it is very difficult to hand stitch through the fusable product.
there are also many tutorials to show you this technique-
search for 'fusable applique', machine applique, or raw edge applique