The shop has no application and no clearnet checkout, so the browser is the whole client. Four settings decide whether the first screen opens at all.
Install the official build
From the Tor Project site or its own hidden service. A browser that merely uses a Tor proxy is not the same tool and does not carry the same guarantees about fingerprint and circuit handling.
Set the level to Safer
Safest switches JavaScript off, and the check screen in front of the market needs it for its half minute. Safer keeps scripts for the top level of a page, which is enough for that screen.
Paste, do not type
The label is 56 characters. Bookmark it after one successful visit instead of entering it again, and compare the banner inside with the string in the bar.
Add a bridge if the network itself is the problem
Where a provider blocks Tor traffic, a obfs4 bridge in the Tor Browser settings is the setting that changes, not the market address.
What the first screen asks for
Before the shop there is a check: a dark screen with the market name, a moving figure and a wait of about half a minute. Behind it sits the account screen, and that one asks for four things, none of which is a password: a name you invent, a PGP key you paste, the picture captcha and a withdrawal PIN you set yourself. What the account does not ask for is an email address or a phone number, so there is nothing to leak from the signup itself and no mailbox to lose.
Once inside, the layout is the usual one for this kind of market: categories on the side, a search field at the top, the balance in the header, and a switch on the home screen that separates physical goods from digital listings.
Tor questions
Which browser do I need for Nexus Market?
Tor Browser, the official build, with no other extension added and no ordinary browser used as a shortcut. A 56 character .onion label does not resolve through a normal browser without a Tor connection behind it.
Why does the shop complain when I set the security level to Safest?
Safest disables JavaScript, and the check screen in front of the market runs a small script that finishes in about half a minute. With scripts off that page can sit there forever, so the level that passes the check is Safer.
Should I use a VPN in front of Tor?
It is optional. If you keep one, the order is the VPN under Tor rather than instead of it, and nothing about a VPN replaces the address check.
Is a phone enough?
Tor Browser runs on Android, and the market is a normal web interface, so yes. What does not exist is an application to install: the shop has no app, the browser is the client.