"what should be my next moves after I “click” to go bronze?"
This is a very interesting and difficult question. You have tons of options at this point and I'm sure almost every answer will say that you have many options and it really depends what's going on in the game.
Above all else scout. Scout like mad. And did I mention scout. Knowing where your opponent is and what age they are in is critical to knowing what to do. If your opponent tools at about the same time as you, you can assume that they will hit bronze at about the same time. If they're already in bronze that's a different matter. Every option you have is directly affected by what your opponent is doing. And I can't stress this point enough. My second tool building is almost ALWAYS a stable. I need a scout or 2 to find out what is happening and what I should be doing.
For instance: Say that your opponent has just barely reached tool (having overboomed or having a horrible position). Or maybe they are on the same course as you and are bronzing almost at the exact same time. Then perhaps it is worthwhile to invest any excess resources you have during the upgrade in what has been called "resource equalisation". Build a few tool units (you should be forward built with at least a 2 military buildings) and go harass him. This will do 2 things. First he might think that you are tool rushing and therefore delay going bronze (if he hasn't already) because he fears your rush will leave him with no econ when he gets there. Second it will definately delay his bronze (running villagers aren't building 2 tool buildings for his bronze or collecting resources he needs to get his bronze army). Then when you arrive in bronze, you should attack with what you have the resources to produce (cavs, chariots, etc). If your opponent can't bronze and/or has no economy you're definately ahead. Make sure that you've taken the seas (if applicable) That means destroying any food production on the sea. This is why taking out woodcutters is so important. He without wood cannot fight or gather food on the seas.
Or perhaps your opponent has tooled and is already half way to bronze. Tool rushing isn't going to be useful here so maybe it's a good idea to defend. Wall like mad and buy enough time to get your army going before your opponent can hurt you badly.
Maybe your opponent is tool rushing? Defend and buy time till your superior bronze units (and hopefully still superior economy) can kill them. Or maybe it's a good idea to hold off the bronze upgrade for a while until you're safe.
If you're going for composite bow or something else that requires a while to get going, it will take a while even after you bronze before you get your army out. Can you wall during the transition? If your position isn't wallable can you relocate to somewhere that is? Can you build a small tool army to hold them off while you get your bronze army going (slingers can take out chariot archers for instance) This advice is also applicable to being tool rushed.
Remember to keep building docks all over the map and boats. Having tons of food in bronze is imperative. Against any player of worth you can expect at least a few villager losses. Keep your economy going. Get the market bonusses that you need. Every economic bonus pays off later.
It's important to remember in all of this that your opponent (assuming it's not a newbie) has a plan too. Will your opponent also resource equalise? What will they rush with? Is it better to build a tower to defend against a small force of archers or axers to deal with slingers or what? If your opponent attacks you (and trust me they will either now or in bronze) Can you run? Have you walled? Do you have a defense set up at home?
Whew that's a lot to do during the tool->bronze transition... Now about what to do when you actually hit bronze. Firstly and possibly most importantly, get the wheel. The reason for this has nothing to do with chariots and everything to do with economy. Every second you have the wheel that your opponent doesn't is like having 25% more villagers working than you actually do. The next thing to remember and perhaps the most important:
DON'T STOP MAKING VILLAGERS!!
I can't believe how many games I've won because my opponents stop making vills after they bronze. (You can tell this... people end up with 40-50 villagers highs in the achievments at the end of the game then they're probably forgetting to pump vills right after they bronze) They just forget that economy is about 50% of the game. Sure you can't amass a huge bronze army right away, but your investment more than pays itself off within a few minutes. Build econ while you're attacking. Get a government center. Build TC's all over the map. Boom like mad. Your ships should be bringing in food, but remember to keep land based gathering going too (in case your opponent finally retakes the sea). Finally you have about 60-70 vills plus a decent sized army. Are you winning comfortably? If so maybe it's time to consider going iron and mopping up. Otherwise keep building vills and keep fighting. Your opponent is probably doing the same thing. Just because you've gotten one of your opponent's bases doesn't mean you've won. They probably have more. Keep searching. Scout scout scout. Make sure to keep your vills productive. It's impossible now (at least for me) to keep track of that many vills and a military. Just make sure that every group is doing something. Try to think ahead and guess what you'll be needing next, gold, food, wood, stone? Put up a tc next to resources every available chance you have. Reasonably you don't need more than 85 vills in a 125 pop game. Or maybe 105 in a 150 pop game. I'm not an expert on managing economy... The important thing to remember is that the players who win later in the game are those who have the largest and best econ. Spread out over the map. If your opponent takes one base you should have several more.
OK this is rivalling Staffa for the longest post so I'll cut it short here. Maybe one of the better players (I'm fairly average) like Staffa can post a complete guide to bronze to point out anything that I've said that's inaccurate or misleading or add some useful hints. *hint hint* Also I've avoided the question of how to fight in bronze as it's pretty race specific. The important thing is to keep your econ going while crippling your opponent. This advice applies at any time in the game from tool till iron. It's the main objective of the game (IMHO). Anytime your opponent is crippled and your econ is still pumping you can build a larger army than them and crush.