Playing now at Prince as well, I often ignore a (relatively) large number of early techs, only going for ones I need. When I get Alphabet, I'm in contact with many enough AI civs that I can immediatelly look for trades. I probably am tech leader now and should have something to trade around if I want to. If not now, at least soon the AI will have nice techs available on branches I haven't traversed, so I (hopefully) can get them and fill the trade with some older techs (both ways).
When I get Alphabet, I'll first check if there are some techs I would be interested in, but will probably trade more fillers when I've got Currency as well, allowing for balancing with coin as well.
Also at this point it's getting important to think about alliances. Early religions have been founded, and most AI civs have converted to something or other. Those who don't have their own religions to spread around are probably shaky though, easy to convert with just a few missionaries. However, the religious blocks are now starting to form, and religion is a big issue in the alliances. So, look at the groups that are forming, think about which you do or do not want to please, and plan your trading partners accordingly. It's just fine to make a "Fair" (as in, AI benefits a lot) trade for some diplo bonus when trying to align yourself in the groups, and it's better to avoid trading with worst enemies of those you want to befriend.
With that in mind, I probably end up paying more than I'd think of as fair, to get the trades going in the group I've chosen as "friends".
Still, not all techs are traded by AI, at least not soon. Some leaders are willing to trade their cutting edge techs (for your cutting edge techs mind you, not some old throw-ins) while others keep them for quite long. The diplo factors weigh in heavily too, so even the same leader, given same tech balance, will react differently based on how you've aligned yourself. And sometimes the AIs manage to do a decent amount of tech trading amongst themselves, surprisingly focusing on different branches of the tree. In those cases you just have to keep checking the tech situation every turn to have a chance to cut in fast and taking the middleman cut from new techs your friends have researched. Pay a lot for a good tech if you can then trade that to some others getting back on your investment - diplo bonuses for fair trading with several civs and a number of reasonable techs for one very unbalanced initial trade.
Other choices? Don't trade. Research yourself. Be a man. Be Tokugawa

Researching everything yourself instead of trading techs isn't impossible by any means. It does slow the overall teching speed though, as human players often go for different techs than the AI allowing for trading at the cutting edge. Not trading doesn't mean that only you will be teching slower, the AI civs will also have to research techs you'd usually have available for trading with them, slowing their teching rate as well. They might go on for quite a while without those techs, but eventually they'll have to research them. Mostly techs aggressively researched by human players can't really be ignored for very long by the AI either.