Catching garter snakes, indeed any specues of snake, isn't easy but there are a few guidelines which will increases your success rate considerably.
Garter snakes favour moist areas with still water in general, with woodlands, bogs and ponds all being possible hunting grounds. So go catching garter snakes in these areas rather than searching around hot, dry areas.
All reptiles are cold blooded - so the warmer they become from basking in the sun the faster they move.
Therefore if you try catching garter snakes early in the morning just as they're coming out of their night-time hiding places they'll be much slower than later on in the day.
There is a range of equipment you might like to take with you when catching garter snakes.
A soft net and/or forked stick will help to trap the garter snake. Either place the net over thw hole body of the snke (meaning you'll need quite a large net) or place the froked end of the stick over the back of the garter snakes neck - so not only pinning it to the ground but also disabling it from biting you.
Or you may like to try just jumping straight in - Steve Irwin style - catching garter snakes gently by the tip of the tail before securing them in a pillow-case or other soft fabric bag before taking them home.
Remember that if you're not 100% certain you'll be safe handling a particular snake it's better to be safe than sorry by grasping it around the next / back of the head area so there's no risk of a bite.
Snakes sense vibrations through the ground so if you trudge along through the undergrowth like a troll you'll soon care away any garter snakes within miles!
So wear soft shoes, and take small, gentle, slow steps, taking care to avoid treading on any twigs, and constantly scanning around you with your eyes for any garter snakes hiding nearby.
The Right Direction
The jacobsons organ lets garter snakes "smell" the air around them. This is what the tongue is doing as it flicks in and out.
That means that if you're wearing strong deodorant and the wind is blowing then any garter snakes downwind of you will have smelt you long before you get close.
So travel into the breeze and leave your toilettries at home.
Finally, when you do eventually some across a garter snake worth catching, approach slowly, as low as possible (stoop close to the ground) and from behind the snake to reduce the chances of it seeing you before you get close.