How to get bigger arms

Do your big lifts first in your lifting routine which will help all your muscles to grow.
I think using free weights over machines is better, because they will require more control from stabilizing muscles. Understand also, that when you do your compound exercises your arms will get worked no matter what.
When your doing a pulling move, such as rows or pull ups, your biceps are getting work in assisting in those exercises. You will not perform well on your compound exercises if you do your isolated arm exercises first. Use your isolated arm exercises to finish up and polish the arms after you’re finished with the compound exercises.
Pre-exhaustion training is where you reverse the aforementioned plan. Tireing out the arm muscles first by doing an Isolated arm movement, will cause the main driver of the compound movement to work harder because the pulling or pushing power of the arms will be reduced. For example: you could do sets of tricep extensions before doing bench presses. The idea here is that, since you biceps are tapped out, your lats will have to work harder to perform the movement. It sounds like a good idea, but, does it really work? Try it out and see what you think.
If you’re finished with the big compound moves, then it’s time to move on to the arm exercises to get big biceps. Hit your arms from as many angles as you can, but don’t over do it. I like to do a standing curl to hit the middle portion of the biceps; a decline curl (about 10 – 20 degrees off vertical) for my biceps to get it in the stretched position; and a concentration or spider curl to really hit the peak contraction point. By the way these are all supinated, or palms up.
You can superset your biceps with similar three position tricep exercises. For instance an overhead triceps extension for the stretched position; a standing triceps pushdown for the middle position and a triceps kick-back for the peak contraction position.
Choose what position you wish to work that day; middle , stretched or peak contraction and just do 3 to 4 supersets of that position that day. The next time you hit arms, do a different position and keep them rotating each workout. And don’t forget a few reverse curls to warm things up.
To hit the brachialis muscle under the biceps and maintain good balance in the arms, turn your hands palms down. The brachialis is the workhorse in the upper arm for flexing the elbow. By turning your hands palms down, you eliminate the biceps and concentrate on the brachialis. If you make the muscle under the biceps bigger, it will push the biceps up and make it stand out more.