There are a number of simple ways to fudge die rolls.
The easiest way to cheat is to simply lie about a die roll. Ideally, the die should be disturbed or scooped up before any observer can verify the number.
A way of indirectly influencing a die is to make arithmetic errors when calculating modifiers to a die roll. Ideally, calculations are chosen which are painful for others to recreate.
When rolling, do not roll all the dice simultaneously, but pour them out gradually. Aim the falling dice at any low rolls already on the table.
One method of altering a roll is very simple. As the die stop rolling, quickly flip over any die that comes up with a 1. You can wait till others look away, or simply move your hand over rolled dice while your other hand continues to manipulate the remaining dice. The movement is so quick it is virtually impossible to notice out of the corner of one's eye. It requires no precision, since anything is better than a 1.
Like flipping, but keep in mind that is is slower and easier to observe. Remember that most dice are designed such as that the two sides sum up to twice the average roll. For instance, the 3 and 4 are opposite on the d6. Thus, a 1 is opposite the high number.
With a few hours practice, most people can practice "rolling" a die with a simple double or triple flip that reliably lands on the desired number more than half the time. Although rarely practiced, deliberately rolling specific numbers is not terribly difficult, and can be picked up accidentally just from handling dice a lot. The only countermeasures are when someone insists you drop the dice straight down, roll into a cup, roll against a wall or screen like a craps player, or otherwise disturb the die's original trajectory.