The following 4 scenes are inspired by a nice set of figures in Stryer's biochemistry textbook (https://www.ncbi.nlm.nih.gov/books/NBK22580/figure/A322/?report=objectonly). In an alpha helix, the main chain arranges in a with the side chains (green) pointing away from the helical axis. The alpha helix is stabilized by from amino acid n to n+4. There are . In space filling depiction, you can see how the main chain is (no space in the middle).
Apart from the characteristic hydrogen bonding patters, the other identifying feature of alpha helices are the main chain torsion angles phi and psi. If you plot phi against psi for each residue (so-called Ramachandran plot), you find that the phi/psi combination found in alpha helices fall into one of the three "allowed" (i.e. observed) areas for non-glycine residues. For a more detailed explanation, see Ramachandran Plot or http://www.cryst.bbk.ac.uk/PPS95/course/3_geometry/rama.html.
Which amino acids are found in alpha helices?
Proline is a helix breaker because its main chain nitrogen is not available for hydrogen bonding. Amino acid side chains whose movement is largely restricted in an alpha helix (branched at beta carbon like threonine or valine) are disfavored, as is glycine. Here is an example of a at the position of a . Prolines are often found at the beginning or end of an alpha helix, as in this example of (this is an ultra high resolution structure where hydrogen atoms - white - are resolved and some atoms are shown in multiple positions).
Alpha helices in soluble (globular) proteins
Example: myoglobin
Example: DNA binding
Alpha helices in transmembrane proteins
A common fold found in transmembrane proteins are alpha-helical bundles running from one side to the other side of the membrane. An alpha helix of 19 amino acids (with a length of about 30 angstroms) has the right size to cross the double-layer of a typical membrane. If the helix runs at an angle instead of perfectly perpendicular to the membrane, it has to be a bit longer. There is a write-up on opioid receptiors in the Molecule of the Month series by David Goodsell (http://pdb101.rcsb.org/motm/217).
Alpha helices in coiled coils
Coiled coil
Gcn4