A Christian can worship anywhere in the sense that prayer is worship and prayer can be done literally anywhere and at any time.
As far as more formal worship goes, Christian worship is generally done at church services. This can be done in actual church buildings, but it can also be done in other places where a church group is allowed to meet (here in my town, church groups even meet at a local movie theater). Christ is quoted as saying that a church is wherever "two or three are gathered in my name."
Most Christian sects worship on Sunday.
In Roman times worship was conducted in outdoor meeting places and in people's individual homes. The first church wasn't established until C. 250 AC where the first excavated church structure seems to be the one at Dura-Europos in Ancient Persia. Christians before this time met and frequently gathered in outside structures and either stayed there or went back to people's homes to either conduct some type of ritual service such as lighting candles or lighting ornaments, and then dsaying a few prayers. Our contemporary view of having official church services inside structures of churches or temples highlight the orthodoxy and structure of the present-day Catholic Church
In a church or they can go on a pilgrimage