How do I bring 50 amp service to my detached garage?
This is quite feasible to do

The hardest part about a job like this is getting your wires down the conduit.  Even with that, though, I would use conduit for the full length of the run to keep things simple.  Schedule 80 PVC is likely the easiest and best solution for a mixed indoor/sheltered/buried run like yours -- it is rated to protect wires against physical damage, is weatherproof, and assembles much the same way that PVC plumbing pipes do (i.e. with cemented joints).  Just keep three rules in mind:


PVC will do the worm on you due to thermal expansion if you don't put expansion joints in every 12' or so in the exposed (i.e. not buried) parts of the run.
Conduit needs support -- for PVC, attach it to the wall or deck joists every 3' and at expansion joint locations.
Keep the number of bends between pull points to a minimum.  Code only allows a single loop (360 degrees), but less is better -- you can use conduit bodies to change direction and reset the bend-count at the same time, provided they're accessible later.


Once the conduit's in, along with a pulling-string to help you get those wires in it, it's time to get some conductors in there.  You'll need THWN wires as the conduit outside is considered a wet location, and four of them at that: two hots, a neutral, and a ground.  The neutral must be white, and the ground must be green or preferably bare to save conduit space, while the hots can be any other color than white, green, or grey.  As to size, you're looking at 6AWG copper or 4AWG aluminum for the hots and neutral, and a 10AWG copper wire for the ground.

Last but not least -- you'll want to size the conduit generously, and a 1.25" PVC conduit will easily fit 3 4AWG aluminum wires and a 10AWG copper ground with room to spare.  Of course, if you want to put in a bigger conduit, knock yourself out -- it'll pay dividends if you want to upsize the wiring or pull more conductors later.