Step 1: Find valence e- in all atoms. Add them together.
B-3
Cl-7x3=21
Total=24
Step2: Find octet e- for each atom and add them together.
B-6 ( exception from octet rule)
Cl-8x3=24
Total=30

Step3: Gives you bonding e-. Subtract step 1 total from step 2
30-24=6e-
Step 4: Find number of bonds by diving the number in step 3 by 2(because each bond is made of 2 e-)
6e-/2= 3 bond pairs
Step 5: Find the number of nonbonding (lone pairs) e-. Subtract step 3 number from step 1.
24-6= 18e-=9 lone pair
Use information from step 4 and 5 to draw the lewis structure.
Put atom with lowest electro negativity in the center. Arrange the remaining atoms around it. Finally put the bond pairs and lone pairs of electrons on the atoms.

Lewis dot structure of BCl₃

Alternatively a dot method can be used to draw the lewis structure of BCl₃.
Calculate the total valence electrons in BCl₃ molecule.
B=3,Cl=7x3=21
Total=24
Put Boron in the center and three fluorine atoms on the sides.
Put a pair of electrons connecting the side atom with central atom.Pur remaining electrons on the side atoms.Make sure each side atom get 8 electrons to get octet state.