Possible signs of an infection are a poorer Internet speed, unrequested visits to websites or unwanted popups and adverts, or even that you can no longer access websites using common browsers. However, infected computers do not necessarily exhibit these symptoms and users very often do not notice anything which might them think their computer has become part of a botnet.
In the Internet you can find then free tools to use to check your computer and remove botnet infections, in addition to using your baseline antivirus.
When you use a dedicated tool for detecting and removing botnet infections, It is a good practice to assure that you have downloaded from an original site by a well-known supplier of security sofware so as to avoid using an uneffective scan tool or a tool that might even contain malware.
In this page you can find some examples of free tools.
Once you have checked your computer protect it to prevent future infections.
Notice that it is important you also read the terms of use of this website.
Notice that no tool can guarantee certain discovery and removal of any infection, since it might be not up to date with the most recent malware. If you suspect your computer might be infected, despite no proven infections are detected by the latest scans, you might consider formatting and reinstalling your system. In this case it is important that you already have an up to date backup of your data.