You need SOLIDWORKS (latest version preferred) to give the exam. It can be at home, office, friend's office or even VAR's office/machine.
Look online in the instructions for the exam preparation and be sure you understand all the requirements.
I have not taken it but I think all exams require dual monitors and fast enough internet connection.
They can, as Deepak Gupta explained, be taken anywhere but you need to be sure you are properly setup first.
If your connections are not correct or too slow, you may time out of the exam and you will not be able to retake it for 30 days.
I believe the CSWP is a 3 part and each part can be taken in separate sessions but it your fail one or more you have to wait to retake it.
As Rick McDonald mentioned about dual monitors they are not required but recommended.
Always use latest Tester to give the exam.
Here are some articles/websites related to CSWP
And finally, these are two free sample exam for trial and self-training via Tester
I would add SolidProfessor and they have recently partnered with SOLIDWORKS to provide SolidProfessor members with an opportunity to earn free Certified SOLIDWORKS Associate (CSWA) and Certified SOLIDWORKS Professional (CSWP) exam vouchers!