Can anyone convert to Judaism?
Yes.
Are there any special requirements or procedures?
Yes. There is significant education in Judaism required. Among the Orthodox and Conservative, women will need to go to a ritual bath, and men will need to be circumcised. If they are already circumcised, a small ritual cutting will be required. Reform, IIUC, will require ritual baths, but will not always require circumcision. At the end the convert will need to appear before a court of rabbis to ensure all requirements have been met. Among the Orthodox, a convert will be turned away three times at first - to ensure they are really serious.
If a former Christian or Muslim want to practice Judaism will it be possible?
yes.
Will Orthodox Jews accept people born into other faiths?
Officially yes. Some individuals may be less accepting. My sense is that acceptance will be greater among the Orthodox, as to them Jewishness is much more about following Jewish ritual laws (kosher, shabbat, etc) and less about culture and upbringing.
Or does being a Jew mean that you have to have Jewish lineage?
See above
Also, if Jews are in fact God's chosen people, then why practice any other faith, but Judaism?
Other peoples may be chosen by God for other destinies. Jews are chosen to follow the Torah, that does not mean God only cares about them.