Start by getting Tor Browser from torproject.org, the only place to install it from. Verify the download signature if you are the type to check things, then run it. Keep this window separate from your everyday browser. The two should not share tabs or history.
Setting the security level
Click the shield icon next to the address bar and open the security settings. Move the slider to Safest before you load the market. At this level Tor blocks scripts and graphics from external origins, which is exactly what you want when a page is asking for your password. The market interface is plain HTML and forms, so it still loads fine.
Loading the mirror
Copy one of the three mirrors from the list on this site and paste the full string, including the http prefix, into the address bar. Press Enter. The circuit builds in ten to thirty seconds. Then the anti DDoS challenge appears, a small element that fills up over about thirty seconds followed by a captcha. Keep the tab open. Do not refresh it. Interrupting the challenge restarts the whole sequence.
Verifying before you log in
Once the page renders, go to the footer or the announcements section and read the operator PGP fingerprint. Compare it to the value on this page, 7699 F8D1 124E E4C6 050C 1DC7 76F2 8225 1486 EFD9. If it matches, enter your credentials or register. If it does not, close the tab. You are on a clone.
The first full load, from paste to logged in, takes somewhere between thirty and ninety seconds. After that, subsequent visits are faster because the circuit is warm. Budget the extra time the first time rather than assuming a slow load means something is broken.
FAQ
Do I need any software besides Tor Browser?
No. Tor Browser is enough to reach the market. You only need PGP tools if you want to verify signed announcements or encrypt messages to support.
Why does the first load take so long?
Two delays stack. The circuit build takes ten to thirty seconds and the anti DDoS challenge adds about thirty more. Together that is the thirty to ninety second window.
What if the captcha keeps failing?
Wait twenty minutes and try the next mirror. A failing captcha usually means your route is flagged, not that you did something wrong.
Can I use a phone instead of a desktop?
Yes, with the official Tor Browser for Android or the Onion Browser on iOS. Do account setup and large withdrawals on a desktop and use the phone for checking orders.