There are a bunch of way to put down pavers, some more effective and more work, some less. Question comes down to a trade off of how much time effort and money now vs how long do you want them the stray exactly where you placed them.
Given what you stated above, I would go about it this way. (I over kill things a little because I am cheap and lazy and refuse to put time, effort and money into something a second time.)
Dig a trench 4" - 6" wider than you pavers and deep enough to hold the paver, 2" of sand or stone dust and 4" - 6" of paver base, processed gravel or crush-n-run. The better and wider you build the base, the longer the stones will stay flat and level.
Once you have the trench done, line with heavy landscape fabric in a "U" shape. You want to have the fabric just short of the top of the soil level of the grass side, (1/2" or so down from the surface), across the bottom of the trench and back up the garden side to about 1/2" or so from the surface. This does 2 things: 1) keeps the fines from washing out of your base and sand which keeps the stones set better longer. 2) makes it a lot harder for the grass to creep in and the weeds/garden to creep out.
Next step is to add 4" - 6" of course base and tamp it down well (2" at a time allows for better compaction and long term stability.
Next step is to add the sand. DO NOT USE "PLAY SAND" or any round grain sand. You want this to lock up against itself so builders sand / cement sand /stone dust are the better option. Add in your 2" and tamp it down well if it is a bit damp, almost moist it will compact better. Hopefully you will have gained 1/8' - 1/4" of space. you will need the space for wiggle room when actually setting the pavers.
To set the pavers, string a line where you want the front edge, add enough sand to under the paver got get it just above where you want its final resting place. Beat it into place with a dumb-dumb or rubber mallet. Make sure it is square and level. Sure a paint stirring stick or similar against the edge to space out the next and set the next stone as you set the first. Once the second stone is set, fill the joint with the sand. A folded piece of cardboard of a make shift "pastier bag" or ziplock with a corner cut off make this easier.
Once all the pavers are set, sweep sand into the joints and water the pavers with a lawn sprinkler. this will wash the sand into the joints and help it settle. You may have to repeat this step a couple of times to get the joints filled.
Once you have the joints filled at least once, front fill the grass side with soil and press the fabric up against the stone and trim to about half the stone thickness. Do the same for the garden side.
Its a lot of work, depending, but the better the base you put under them is directly proportional to how soon you will be out there messing with them again.