Alden Armagnac, a former Popular Science editor, enumerated several tricks for multiplying large numbers in a 1967 issue of the magazine. If you're multiplying two large numbers, double one and halve the other. For example, multiplying 16 by 35 is easier if you halve 16 to 8 and double 35 to 70. The resulting 8 times 70 multiplies much more easily in the head to equal 560. While not all numbers halve and double as easy as these, often they do.
Changing awkward multipliers to a near-round number simplifies calculation. So if you want to multiply 29 by 63, just change 29 to 30 and multiply that by 63, which equals 1890. Now, to compensate for the change, multiply 1--since the difference between 29 and 30 is 1--by 63. Then subtract 63 from 1890. Granted, 30 times 63 still may take some time for those not accustomed to mental multiplication. But the piecemeal approach still simplifies the equation.
A refinement of the piecemeal method, the stepping stone method works in some instances, such as when multiplying a number by 15. By treating 15 as 10-plus-5, you only need to multiply another number by 10--which is really easy--and then cut it in half--also easy--and then add the two products. So, for example, 15 times 29 would be 10 times 29 (290) plus .5 times 290 (145), which equals 435.
Sometimes you might only be looking for a "ballpark" estimate when multiplying large numbers. In this case, you only have to work with values of 10. For example, 526 times 385 could be expressed in stages, first multiplying by 100s, then 10s, and then adding the products. So, first, multiply 500 times 300, which equals 15 plus four zeroes, or 150,000. Next, multiply the tens in the smaller number (80, from 385) by the hundreds of the larger number (500, from 585), which equals 40 plus 3 zeroes, or 40,000. The numbers 40,000 plus 150,000 equal 190,000, which is well within the ballpark of the exact product: 202,510.