Below is a photo of my personal collection of dumbbells which I use for weightlifting at home.
Also in the photo is my weightlifting gloves. They are my "Atlas" weightlifting gloves, which I sometimes also use for cycling outdoors, and also my "Copper Canyon Cycling" gloves, which are basically identical to the Atlas weightlifting gloves. It doesn't really matter what brand you buy, the gloves are there to protect your hands so you don't hurt yourself / develop painful callouses. The gloves cost about $10 to $15 and are totally worth it.
All the dumbbells shown here were purchased at Canadian Tire - they cost about $1 per pound. Thus if you are doing the math I have spent $105 + tax on my dumbbell collection. Plus an extra $30 on gloves.
Once you have your dumbbell collection, what do you do with them?
This is easy. Just do 8 to 10 repetitions. Rest. Repeat 8 to 10 repetitions. Rest. Keep doing that 5 to 10 times. Doing between 40 to 100 reps of bicep curls every 2nd day (combined with a healthy balanced diet) will help you build bicep strength pretty quickly.
#2. Tricep Raises
Using one or two dumbbells lift your arms above your head and lower your the dumbbell(s) behind your head. Lift it back above your head slowly. Lower. Repeat 8 to 10 times. Rest. Repeat 5 to 10 times. Doing this exercise every 2 days will build up your tricep muscles quickly.
#3. Shoulder Raises
Using a lighter dumbbell - something you can handle more easily - hold the dumbbells at your sides and lift sideways until they are at 90 degrees. Lower slower back to your side. Repeat 10 times. Rest. Repeat the exercise 5 to 10 times. This exercise will build shoulder strength quite rapidly.
Taken together these 3 exercises will help you build strength in your arms and shoulders quite rapidly - but they should not be the only exercises you are doing. Push ups, chin ups, and sit ups are nice additions to the above 3 weightlifting exercises. The push ups will build your arms, shoulders and pecs. The chin ups will build your arms, shoulders, back and pecs. The sit ups will build your abdominal muscles.
Pay attention to your form. Good form avoids injury and builds muscle faster.
Stick to dumbbells you can use. If they are too heavy for you to complete all the exercises then you need to be using a lighter poundage.
Explore other exercises too, including other ways to utilize your dumbbells. Examples include the Zottman Curl, Y Press (lifting the dumbbells to make your body into a Y shape),
If you experience any severe pain stop immediately. Wait two days before weightlifting again. Excessive weightlifting can cause severe muscle fatigue - which can lead to injury and chronic pain.
Eat a protein bar or protein shake after finishing your weightlifting routine.
Eat healthy - including veggies and protein! Weightlifting without eating healthy is like buying a muscle car, but forgetting to buy gasoline. Your body needs fuel to grow muscle.
Challenge yourself. If your dumbbells feel too light, it is time to get a dumbbell that is 5 lbs heavier. Don't overdo it, but aim to challenge yourself physically.