Multiple connections to a router typically don't result in slower Internet access unless the combined speed of downloading reaches the top speed of the Internet connection. For users browsing websites on a high-speed connection, this is rarely an issue.
If two users are downloading large files, streaming bandwidth-intensive videos or playing games, they might notice a slower connection. Quality of Service and other technologies, however, can help provide smooth overall performance. Routers and other networking hardware are designed to handle a large number of connections simultaneously, but connecting too many devices can saturate the relevant wireless frequencies and push the router's processor beyond what it can handle. However, this scenario is unlikely for most homes.