If you are using After effects CC, click on composition>Add to Adobe Media Encoder Queue
Click on format and change it to MPEG4.
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You need to learn about encoding. The default file type is Lossless for a reason. If you are using Ray-tracing and you have a supported Cuda card you must use the Adobe Render Cue. If you are not using Ray-traced rendering then you should be using the Adobe Media Encoder.
This will get you started: Basic Workflow, the last section is on rendering.