Lactic acid is an alpha hydroxyl acid (AHA) used to exfoliate, lighten dark spots, and improve fine lines and wrinkles. This is achieved due to its  capability of speeding up cell turnover and cell renewal where new cells replace old cells. When old cells are replaced, the  pigment-stained cells are replaced with new clean cells, this reduces and fade the appearance of dark spots and hyperpigmentation and filling up fine lines.
When used regularly, it can do wonders for the skin and is one of the most gentle hydroxyl acids among the others.
Lactic acid peels are often performed by a dermatologist or aesthetican , but light, superficial peels are safe to do at home. 
It is advisable as a first user to start low by using a mild lactic acid concentration and study how your skin tolerates the peel then concentration is gradually increased .
Warning:
Do not use this professionally grade peeling solution  without a professional supervision if you have;
sensitive skin, 
facial scars 
recurrent cold sores, 
medical problems 
pregnant/breast feeding. 
Do not perform an at-home peel without talking to your aesthetican  or dermatologist first.
If you take prescription medications, speak to your doctor before using a lactic acid peel.
Usage guide For LACTIC ACID PEEL.
This is a general guide, a professional would normally analyze treatment skin and recommend the best way to use product to suit client’s skin problem.
The lactic acid needs to be applied on the skin , few minutes needed for the skin to absorb the peel and then it is neutralized .
To make your neutralizer, make a 20% baking soda solution by adding 80g baking soda (sodium bicarbonate) to a 400ml of clean water.
Keep this aside as you will be rinsing your skin with this.
For facial peel:
Concentration is determined by the dermatologist according to skin type and treatment type.
-Face is cleansed with a mild soap or cleanser and dried.
-Using an applicator brush or cotton bud, lightly apply the lactic acid solution, avoiding the  lips, nostrils and the sensitive skin around the eyes.
-After 30-60 seconds, you can apply 1-2more layers of the solution depending on how much your skin can take. 
-Leave the peel on your face for one  more minute or more but typically 2-5mins depending on the concentration used and how much solution your skin can hold.
-Rinse off the peel on the face with the 20% baking soda solution (neutralizer)
-Rinse again with clean water and then dry up before applying your moisturizer and sunscreen.
Note that If the lactic acid concentration is as low as 20%, you can leave it on your face for up to 10 minutes maximum while higher concentration may be left within 1-5mins. 
Lactic acid will create  a chemical process that kick starts the skin’s exfoliating process. After the process is completed, skin is left bright and hydrated.
Recommended usage timing is weekly or every 2weeks. Can be also be included in your hyperpigmentation treatment routine . 
For dark armpits;
Apply 20% lactic acid on the armpit 3 times weekly, this will brighten the underarm area.
For faster result, use along with a Depigmenting product. 
For wrinkled dry hands and feet;
For hands and feet, 50% lactic acid or higher may be recommended. 
Make your 20% baking soda solution and set aside.
Apply 2-3layers of lactic acid peel and wash off after 5mins or less depending on your skin.
The peel is washed off with the 20% baking soda solution to neutralize the peel from further action.
Rinse with clean water and apply your urea cream for intense moisture. Do this every week to gradually get rid of wrinkled hands and feet.
For dark knuckle treatment;
Application depends on the concentration being used.
20% can be applied on knuckles daily for 3-5days . After applying the 20% peel, wash off after 1hr.
Afterwards  3-5days, shedding is expected where the skin starts to flake.
 Depigmenting serum or cream is applied after skin has shedded .
If you are using 50% , apply the 50% lactic acid on the knuckles for 3days . The 50% lactic acid is applied and washed off after 10mins. 
On the 4th day, start application of Depigmenting serum or cream to fade off pigments off the knuckles while the top layer of the knuckles peel off.
Peel can always be applied a month after if not satisfied with result. 
Moisturizers and hydrating serums will also help as the skin needs a well hydrated environment to function properly, else it can be easily irritated and give birth to inflammation which could cause more darkening.
Note: This is a general usage guide, users are advice to tweak use according to their skin type, skin area and skin treatment.
Warning: Lactic acid can  make your skin photosensitivite, it is advisable to always use sunscreen during the day and avoid too much sun exposure to avoid sun burn.