You can use dumbbells or kettlebells for this movement. The nice thing about using kettlebells is the weight is not balanced so it should offer you a little bit more of a challenge.
Referring to picture one, start tall with your shoulders forward and hips forward, holding the kettlebell in your right hand. Hinge your hips back, bending the left leg slightly (sitting back on your left hip), drop your torso forward while letting the right leg go straight behind you into a single leg deadlift (SLDL), squeeze your right glute. As your torso drops forward let the kettlebell reach down towards the inside of your left ankle. Doing it this way is a little bit more challenging because of the anti rotation forces you need to control. You have to fight, stabilize and focus to keep that right hip pointing forward while staying balanced.
Referring to picture two, start tall with your shoulders and hips forward, but this time hold the kettlebell in your left hand, the movement stays the same as described above, except now the kettlebell will reach down towards the outside of your left ankle. That left leg will feel more stable as the weight helps to balance you on that side. You're not dealing with the anti rotation forces doing it this way (as in picture one) so you may want to go with a slightly heavier weight.
Another option for the SLDL is to have a weight in each hand while performing the movement. This increases the total weight which in turn will make it more challenging. But the weight is now balanced on both sides and this helps you stay steady throughout the movement.
The extra weight makes it more challenging but also helps with balance
Referring to the pictures again, remember to keep your spine straight (no flexion), and your shoulders down and back to stabilize your upper back. This is a hip hinge and if you are doing it correctly you will feel the hip loaded on the side that is stationary. Reach down only as far as is comfortable for you while keeping good form. Don't roll your back just to reach further. Keep in mind that your torso drops down the same time your leg raises behind you, like a seesaw motion, with your hip being the balance point. As you stand up be sure to squeeze the glute tight and keep tension throughout your body. That will help you to stay balanced.
Whether you decide to hold weight in both hands or one, your choice depends on what you're looking for, and whatever you feel like doing on that particular day. There is no good, bad, better or worse way when it comes to doing your SLDL's as I described. Each exercise will challenge you differently.
I suggest you play around with each one. Focus, stabilize, balance and figure out where you need to keep your tension as you go through the movement pattern. It's always a good idea to practice first with no weight. Go through each example and stand next to a wall if you're having trouble balancing.
SLDL's are an excellent way to build strength while balancing on one leg. If one side is weaker than the other this is an exercise that will strengthen the weaker side without letting the stronger side help out. Add these into your workouts at least once a week and it won't be long before you notice improved strength on your weaker side. Do anywhere from 4 to 5 sets of 5 to 8 reps or 4 to 5 sets of 10 to 12 reps on each side.
If you have any questions on this very beneficial strength movement please don't hesitate to ask!
Useful practical information and a workout or two...