There are many different kinds of charts out there, some very familiar from everyday use, while others can be highly unusual, complex, or rarely seen. It's important to use a chart that's appropriate to the data you have, and that allows you to explore the information you're interested in. The Data Visualisation Catalogue can help you figure out the best chart for your situation.
Some common charts include:
Proportional area plots
Tree diagrams and treemaps
Declutter your annotations
You need to make sure that you include enough annotations for your chart to be understood: x- and y-axis labels indicating units, a legend, labels for highlighting important points or trends in the data can be essential to ensure that your chart succeeds in conveying the intended information. However, you should make sure that you remove any non-essential annotations that might be cluttering up your chart. Generally remove gridlines, any background fill, extra tick marks along the axes, busy pattern fills, any colour that doesn't represent information, and any extraneous text. It will be up to you to decide what is necessary to keep to make your chart usable, but keep in mind that having less detail to sort through means that your viewers will quickly see and focus in on the main messages of your visualisation.
Declutter your data
Keep in mind that if you try to put too much on one chart then the relationships that you want to display can become lost. For instance, plotting a large number of lines on a line graph can mean that the trends of all lines become obscured and no information can be taken away from the resulting visualisation. In this case, it would be better to plot small subsets of the data on multiple charts, and compare the charts to each other. Using dual y-axes can also make your chart difficult to interpret, and potentially even imply relationships between variables that are merely artefacts of how the variables were plotted. Any time you feel the data are overwhelming the viewer, assess whether it would be possible to use multiple plots to make relationships and trends clearer. Note that this is not a licence to throw away data that doesn't fit your message! You always need to make sure that you are accurately representing your data, or the whole point of creating a visualisation is lost.
Comparing multiple plots
If you intend to compare multiple plots you must ensure that they have been plotted the same way, are the same size, have same scale axes, and employ the same conventions to enable your viewers to draw accurate comparisons between them. They should also be plotted next to each other, rather than on separate pages or slides.
If you use colour in your charts, make sure that a difference in colour provides the viewer with useful information, as extraneous colour changes can be distracting and make it more difficult to compare the data represented. For instance, don't colour all of your bars in a bar chart a different colour; the different categories are already indicated by the fact that they are separate bars! Either use the same colour for all of your bars, or colour them based on another variable, or to highlight a particular bar that you want to draw attention to. Remember to think about how colour in your chart will affect its usability if it is reproduced in black and white, as well as how your chart will appear to people with colour blindness. Use resources like ColorBrewer to choose colour palettes that are colour blind and black and white friendly.