Foot straps, if on a directional, need to be loose. Else you break knees or most commonly ankles.

Strapless: you're dipping your butt in the water with your heels on the board. Board will stay flat on the water - way easier. As you would waterstart on a twin tip (swinging the kite and all if needed), you water start on a strapless directional. As soon as your butt gets out of water or even a bit earlier, you roll off your heels onto your feet on the board to get full contact and control over the board. You might even be pointing your toes like a ballerina when dipped in the water so you get the full contact quicker when you roll over the board. As you get up on over the board turn downwind if needed, stick the boards edge into the water and ride off. You know, the regular twin tipsy, strapped stuff.

Seriously, it's no different to twin tip nor strapped directional apart from heel to foot. But even then, if it's not too choppy you could even tip the board sideways and keep it sideways under your feet while you're in the water.

Just don't overthink it because it's not difficult at all.

As said it's mostly the same whether you're starting on a twintip and a surfboard/directional. Where it is different is foot placement, both when starting and on the move. All boards are quite responsive to shifting your weight to improve the ride, but at least going strapless your feet aren't locked in so dont be afraid to move them around and find what works best.

I generally lay the board perpendicular to the wind, lay my heels just this side of the board's centre line and just hold it in position with my heels. The downwind pressure from the kite will keep you in contact with the board. I will then bend my legs to bring my arse close to the edge of the board (this allows me to flatten my feet and make better contact on the board) and I dive my kite. By bending the legs during the dive, your kite isn't working so hard to lift you on to the board. Make you sure you are going downwind a bit to build up speed before you start edging upwind.

Once you get good at it, you will find you can swing the board up to your arse with one hand, your legs are already up and bent waiting for contact while diving the kite (big waves approaching encourage this technique!!)

I point the board more downwind compared to the twin tip during start and ride a bit longer downwind before edging. Also found that much more weigh is on the front foot when using directional boards.

hey smoke and mirrors
the main point on water starting for me has less to do with the board and more to do with the kite. practice flying the kite from around 10 up to 12/1 and getting just the perfect amount of vertical float to be weightless above your board (as opposed to having it over your head and dipping it down for sideways pull). once up and weight centered over board, you can put your feet anywhere you like really, and send the kite in the direction you want to go. this works well as a starting style from the shallows (kite starts at 10 in the offshore direction), or i use from anywhere. all you need is bum in water and feet generally in contact with board above, and then control the amount of vertical lift by flying kite up and pulling in bar enough to get up on board. usually need to dip quickly if the board hasn't much volume, more volume = more time to chill and then send it where you want to go.

advice above is all great as well, but i noticed an absence of reference to kite movement, and the vertical float is not something you consciously do water starting a twinny, but probably do instinctively at various times since learning. get practising!