That 40lb dumbell set is going to be exactly useless. You also stand to gain nothing with your parents controlling your diet. If you are serious about gaining muscle, you need to be looking at buying your own food to control your macros, and buying a gym membership to use proper weights.
Building muscle is not hard in theory, but it does need the right input. 90% of the job is diet. Calculate your protein requirements for anabolism (1.5-2g per pound of body weight), more or less match that number with carbs, and get some fats in there too. Make sure the total calorie number is 500-1000 calories above your TDEE (calculators for this and BMR exist online).
Next is weights, and by weights, I mean barbells. A good muscle building program can start with squats, deadlifts, overhead press, and bench press, but expand where you want to.
How you lift depends on your goal. At the end of each set, you should be unable to do another rep with good form, that is how to determine the weight you lift. If you want size, do around 10-15 reps per set (sarcoplasmic hypertrohpy); if you want strength, do around 3-6 reps per set (myrofibrilar hypertrophy). Between 2-6 sets should do it.
Other things to know about weights include:
- Do research proper form, A LOT. It's all too easy to be injured under weights so make sure you do lift properly. Read and read, and then practice with low weights. Build up until you get to your max.
- Do take rest days. Rest is one of the most important and overlooked factors in building muscle. The saying is, "gains are made on the rest days, not the workout days."It's true.
- Do not work the same muscle twice in a row. Most people rotate their body sections, i.e. Monday, chest; Tuesday, legs; Wednesday, rest; Thursday, arms; Friday, deadlifts. Whatever, the point is don't be overworking muscles.
- Do not fear cardio, but don't overdo it either. Cardio does not build muscle, but it does rob calories. It's great for later when you cut, but remember to up the calories to match any cardio you do.
As a newb, you stand to make some pretty serious gains initially, so look forward to that. It's a long game, though, even under perfect conditions, a man only stands to gain 0.5-1lb of muscle a week.
That's about it. It's easy enough, but it does require dedication. The body does not like building muscle, so it has to be forced to do so. Good luck.