Let's think about this.
Here is a hypothetical chromosome 1, already crossed over and about to be split through meiosis2 into two gametes, one of which will produce you.
[ABCDEFGhijklmnop]
[abcdefgHIJKLMNOP]
Background: Crossing over occurs along the non-identical chromosomes, ie: Chromosome 1A and 1B, not duplicated 1A and 1A.
So, before this crossing over, these chromosome would have been in a different conformation, such as
[ABCDEFGhijklmnOP] >>(switched OP)
[abcdefgHIJKLMNop] >>(switched OP).
These chromosomes would be identical to the rest of your somatic cells and undifferentiated germ line cells. The DNA composition of these two chromosomes (one of each would be from your parent's mom and dad) has been directly given to your potential parent. However, these chromosomes (switched OP) would be the product of crossing over in each of your grandparents.
So, you are NOT inheriting genes from your grandparents directly. There is a constant generation of new chromosome sequence via crossing over. You do inherit genetic information from your grandparents, but the exact composition of each chromosome is exchanged.
Therefore, when looking at inheritance patterns and punnet squares and the like, you are completely ignoring in most cases the outcome of these genetic rearrangements.
There is a 'skip a generation' effect that occurs in some (autosomal recessive) cases, where a grandparent may be affected (ie: aa), your parent is unaffacted (Aa), and you again are affected (aa). This is not a rule and just a possibility.
Be certain by common sense that you get your genetic material from your parents. There is a linearity in the process, and this is called a lineage. Don't be foolish to think of biology as something magical... it is pretty down to earth if you understand the basic principles. Good luck!