Taming your Budgie takes lots of time and patience but it can be done. The first thing before taming your Budgie is to clip it's wings. This is NOT cruel in any way for it is not painful and it speeds up the taming process. There are many reasons why to clip your bird's wings:
*Prevents your bird from flying somewhere high.
*Lessens the chance of your bird escaping.
*Lessens injuries from flying into walls, windows etc.

Also many websites and people recommend that you clip 7 or more but only clip 3 on each wing, let them have a test glide and if they still can gain height, clip another on each wing until they can't gain height. They should be able to fly forwards just not upwards.

If this is the first time that you are clipping your bird's wings then I suggest you ask an Avian vet or an experienced breeder to show you a couple of times before you attempt if for the first time.
If you do not have an Avian Vet in your area or you want to attempt to clip your bird's wings, I suggest you research a LOT before you do anything.

Now that you have clipped your bird's wings the taming process shall begin. You should not try to tame your Budgie until you have given it 1-2 weeks to adjust to its surroundings (this is very important and depending on your bird you may need more or less time) There are many ways to tame your bird but most are terrible and just make things worse. NEVER GRAB YOUR BIRD UNLESS IT IS COMPLETELY NESSECARY!!!It wrecks any trust you have with your bird.

The methods I do not encourage to use are the following:
 

Catch and Release:
Take the bird out of its cage when you get it and grab it and release keep repeating this for 30 minutes.
This method does not work for the bird perceives you as the enemy at first and doing this without giving it time to get used to you is just making you seem as the enemy more.
 

The Ultradastic Training Method:
Take the bird out of the cage once you get it and hold it for 30 minutes. The bird will attempt to bite but this will turn into nibbles in time.
This Method does not work for the same reason as the first one. Both of these Methods only teach them to tolerate but not respect and like you.

The following Method I do recommend:
The On Their Own Time Method:
Talk to your Bird soothly every 2 hours or so for 20 minutes for a week. Now put your hand on the side of the cage talking soothly for 20 minutes twice a day or more for a week. Then put your hand into the cage SLOWLY a little bit from the entrance and do not move your hand farther until the bird has settled from your presence. Do this for 20 minutes twice a day for a week. Now only do this if your bird is totally comfortable with your hand in the cage. Put your finger slowly up to the bird's lower stomach and push on it firm but gently and say "UP" if the bird perches on it. If it doesn't perch but instead flies away or runs away then try this again in a minute. Do this every 2 hours or so for short periods of time and only proceed to the next step if the bird seems comfortable perching on your finger. Now with the bird on your finger move it a cm or so away from its perch leave it there for 5 seconds then bring back to the perch saying "DOWN" when it goes back on its perch. Gradually increase the distance until you can take it to a different perch. Do this for about a week more if needed. Now go into a bathroom or a closet and try to take the bird out with your finger. If it doesn't come out just keep trying. Eventually with time an patience it'll come out although never force it. When it is out just practice perching while giving it treats and breaks. Do this for about 30 minutes a day until the bird becomes comfortable with perching on you. Then you may take it to a more open room and keep perching and before long you'll have a tame bird.
This Method works very well for you're working at the bird's pace and not forcing it to be with you it will soon learn to trust you this way and want to be with you.
* If bird nips you in the cage then use a small perch (you can cut of the end of a wooden spoon) then slowly transfer to a a finger once the bird is comfortable perching on the wooden spoon*

My way is not very good for it's forcing it out other than working by it's pace. Please only try this if the above method does not work and for pet-store bought birds expect 4-8 months before it is really tame. You must be patient and work with your bird daily. I tamed my bird's using the On their own Time Method with a slight alteration. I did not teach them "UP" in the cage but outside the cage. I only did this when the bird's were comfortable with me (3 months after I got them) and my presence. I went into a bathtub (you can use a shower stall if you want) and I took out everything from their cage leaving only one perch in there then I popped the cage off and I slowly tipped it down so the bird's had no choice but to get out of the cage or be on the bottom. Then I used a perch (end of  a wooden spoon) and I made them perch (I did this with them separately and where they couldn't see each other) Since the bathtub is very small the bird couldn't run away far. I kept making it perch with breaks in between where I put it on my leg and gave it a treat speaking soothly to it. I did this for about 5 minutes alternating with each bird for about 30, minutes then put them back in the cage. After a couple of days I started to use my finger and before long they would perch with no need to push on their stomach. Then when I thought they were ready I took them out of the bathroom and worked with them in a different room ( make sure there's no dangers in the room) and just played with them, fed them their fruits and veggies and just sat with them. This took about 2 weeks for my birds and now even though they hate coming out of their cage they will come out on a perch but I got to hide the cage or they'll run back to it and they will perch on my arm or finger whenever they see it and will sit on my leg for hours on end.

Taming your budgie is worth it for you'll have a better budgie that will perch on you whenever needed and they won't be scared of you and it will deepen the bond between you both.