Never played AoE3, but got some general tips for SC.
1- Ever hear of APM? It stands for Actions Per minute. It shows how fast you move and click and is indicative of a pro player. A lot of people obsess over getting it up!
Ignore it.
You will probably read a lot about it, but in all honesty you don't need it. (At least until much later levels, so ignore it for now).
2- Play the campaign.
In both BW and SC2, the campaign does an excellent job of teaching mechanics (more on this later) and introducing the player to the UI.
3- Ignore builds (for now)
Builds are important, but at the very beginning, play intuitively. If you have 1000 minerals, make some extra barracks! is his army a lot smaller than yours? Attack!
Not only is this a lot easier, but making up your own ideas when your just learning is a lot of fun!
4- Mechanics, mechanics, mechanics.
Now, what are mechanics? Mechanics are your ability to do simple, essential tasks well. Here are a few simple examples
a. always be producing workers, no matter what. When do you stop? Someone (I forgot who) said "If you have to ask when to stop producing workers, then don't"
b. Always be producing units out of your buildings. More units is good!
c. Try not to queue units. Your structures can queue 5 units to automatically start once the last is done. But if you have say 5 medivacs queued that's 500 minerals and 500 gas you don't have! you can do a lot with that money!
d. keep up with chrono boost/mules/inject larvae. all 3 of these things should be done more or less ASAP, and don't let energy store up.
5- EXPAND! I know this is rather specific, but if you teach yourself to expand, it's like a free pass to gold league. (As a rule of thumb try to start your expansion before 10 minutes)
6- Don't worry about your league. If you are placed into bronze league or E rank, don't worry, just get better.
7- Learn some builds!(Yep, you are now ready young patawan!) There are plenty of helpful pro-gamer vods and streams, go to youtube and look up HDstarcraft or husky starcraft for some somewhat simplified, easy to understand analysis of progames. Feel free to steal a build order from a pro, and try to do it as well as him! while you probably won't be able to do it, it helps your mechanics.
8- have fun!
IF you want to learn more head over here for SC2 BW content
Teamliquid.net (be careful, they have very strict moderation)