The actual speed of impacts can be up to 14 km/s, it is something quite serious, even for small issues. There are a number of procedures taken to prevent such thing.
The first level is known as the "Big Space" theorem, which is that space is really big, and there isn't that many objects. We are getting to the point where this isn't good enough overall.
The second layer is to detect such objects. There are a number of systems that can do this, the best is the system provided by the US military, called JSpoc, or the public outreach called Space Track. They monitor all objects, and will inform parties, both commercial and government, when a predicted impact might occur. These can be predicted days in advance, and allow an object such as the International Space Station to flee a potential collision. This works for objects larger than 10 cm. These sometimes occur too late to be of help, in which case additional actions are taken, see this article.
The third layer is to protect the space around the space station. This is done primarily for the objects visiting the space station, which are launched into a non-intersecting orbit and slowly transition to the final orbit, to reduce the debris in the area. NASA also requests coordination with commercial entities operating near the space station to ensure they are not going to impact the station.
Another layer is provided by selecting an altitude where the space station is relatively low, reducing the lifetime of debris in the area to only a year or two.
Lastly, there is shielding on the space station that will prevent a small item, say a paint flake or grain of sand sized object, from damaging the station. I understand it works until about a 1 cm object. The shielding is called a "Whipple Shield".
All this being said, there is still a substantial risk of damage. Take a look at this graphic, which shows the relative chance of impact.