For the record and for those interested, I want to give a little more detail than is in Leah's answer. Leah's answer is a very good overview and has the important points that a beginning genetic genealogist needs to know. The real world, as always, is a little more complicated.
Our DNA is organized in three kinds:
- autosomal chromosomes (numbered 1-22)
- sex chromosomes (X & Y)
- the mitochondrial chromosome
Autosomal DNA is most of our genetic heritage, being about 93% of it (over all three kinds of DNA by length). It acts just as Leah has outlined: you get exactly half from each parent, but a variable amount from each of your four grandparents.
The sex chromosomes (which are almost all of the rest of the DNA) act differently, as they not only determine sex but their inheritance depends on the sexes involved. A female will have two X chromosomes, inheriting one from each parent in much the same way as for autosomal chromosomes. A male will have only one X, inherited from his mother, and will additionally have a Y chromosome, inherited from his father. A Y chromosome is only about one third the size of an X chromosome, and has even less than proportionately fewer genes. So overall a male inherits about 49.2% of his DNA from his father and the rest from his mother (instead of 50%/50%).
The mitochondrial chromosome is a real oddball. It is tiny, being only 0.0003% of the kinds of DNA. It doesn't reside in the cell nucleus (where all the rest of DNA is), and there are many identical copies of it in a cell. And it is inherited by a child only from its mother.
So, yes, to a first approximation we do get half our genetic inheritance from each parent, and a variable proportion from earlier generations. For genealogy, the most important additional consideration is that the X and Y chromosomes have special inheritance rules that are a bit different than the rest.