Not quite sure how to answer as I don't know why you ask. 1st if the problem is that your charts are only RTH (Regular Trading Hours) then you need a data provider that can give you Globex quotes 2nd you need a broker that has permissioned you for Globex. Some brokers just permission RTH and you have to ask for Globex. Globex charts can cost a bit more but that's basically it. 3rd if you mean how to you trade shares after hours then with the above technology you need to watch liquidity and spreads, because if volume is light you'll pay a lot more to get/out in the market. The blue chips are easy to trade before the open. Trading an hour before the open can be one of the best times to trade. If that doesn't answer your question then be more specific.
All you need is a broker that provides pre/afterhours access to its clients. Just ask your current broker about it. If not then there are plenty of others who do. On a side note, stocks do NOT trade on Globex. Globex is only for futures and options on futures.
US equities are open from 6am to 8pm. Have you ever tried to put in an order in these times? You cannot route it to an exchange obviously, have you tried routing to ARCA during off hours? Pre-open things tend to move. Post-hours only if there is news or earnings for the most part.
Do you know if thinkorswim offers pre-market/after hours? I can trade the futures but haven't attempted it yet.