Perhaps you could try using a method where you break the numbers down into smaller ones, to make it more manageable to do mentally. What you want to develop from doing this, is either an intuitive feel for numbers (meaning you simply know the solution to a combination of numbers and operations without having to work through it), or, you develop a very strong ability to concentrate and visualize the arithmetic in your head.
The goal is to give you the ability to perform these things very quickly, efficiently and probably most importantly, mentally (most preferably intuitively).
To get used to working with arithmetic in your head, it might help to start with smaller numbers or break the numbers down.
For instance:
8+6 -- Try visualizing the number 8 in your head. Now, if you can, break the number 6 into two smaller numbers, such as 3+3.
Try to add 3 to eight in your head (if you need to, keep a mental place of each digit you are adding and simply count).
For instance, you know you need to add 3 to eight, so in your head, count up three places. From 8: 9, 10, 11.
Practice this in your head until you get a feel for it. Then, add the next 3:
12, 13, 14.
8+6=14 -- The work you do is simply count.
If you have to do 8+3 in your head over and over again to understand how to keep mental track of your numbers, then do that until you move on.
After you are able to add in your head 8+3 and then +3 to get 14, try just adding 8+6.
Start with eight and count up six places: 9, 10, 11, 12, 13, 14
Do you see how there are six numbers here and at the end, it equals 14? This is all addition is.
Alternatively, you can memorize your addition tables (if there is such a thing):
1+1=2
2+2=4
3+3=6
4+4=8
... and so on. If you can do this, then you can always use your memorized addition as a point to start from doing harder ones, for instance:
If you know 4+4=8 and someone asks you what does 4+3=, you can easily remember that 8-1=7.
Hence, 4+3=7.