“three-pound dumbbell” / “three pounds”
A dumbbell is a short weight held in the hand, and a pound is a unit of weight. One pound is about 0.45 kilograms, so three pounds is about 1.4 kilograms. When the weight describes a noun, as in three-pound dumbbell, pound stays singular; when stating the weight alone, it is plural: three pounds. Tina thinks this is light and wants to try a heavier one.
“form is more important than weight”
Here form means exercise technique and body position, rather than a document. The trainer explains that learning correct movement matters more than lifting heavier weights.
“Will I get sore tomorrow?”
Sore describes pain, including muscle pain after exercise. Get sore means to develop that soreness. Another use is a sore throat. Tina's question leads into the trainer's reply about her muscles working.
“lying down is part of the plan”
Lie down means to rest lying on your back, and part of the plan means included in the plan. Tina takes the trainer's point that rest matters in the way that suits her best: lying down is part of the workout plan. This leads to her last line, "Especially the resting."
“That's... one way to put it.”
Put can mean to express something in words, so That's one way to put it. means "That's one way of saying it." It is a set phrase used with a wry smile when someone's description is off the mark or exaggerated. Here the trainer responds mildly to Tina, who is delighted that "lying down is part of the plan."