When you first get started, you have the option to use the default region which includes the Mayor Tutorial and the Terraforming Tutorial. Some people may choose to skip these and jump right in but I would suggest going through them and follow it step by step, especially if you haven't played any of the previous SimCity games. Even if you have, it gives you the basics on how to build and connect many items from within your city or how to build your own region. If you decide to not do the tutorial right away and your city continues to fail, go back to the tutorials to see if there might be something you're doing wrong.
The best advice I can give is this: look at the tool you want to use a little closer because there is a big difference between gentle rolling hills and cliffs. That can make a big difference when building your city because some roads/streets/highways cannot get over/through the rough terrain. Some will build tunnels through them but that still makes development above that very tough.
On smaller maps, it is best to have maybe a small creek going through it as the more water you have the less room for development but also without water, your land value won't rise as quickly. On large maps, it is good to have a river running through the middle of the map for a water connection to the other cities, for higher land value, and more recreation.
SC4 seems to have a "rule of 3" which I will explain later.
One thing that I have noticed about smaller maps, it is better to place mostly lower to medium density residential on the smaller maps because it leaves room for jobs for the neighboring cities. Also building that way will allow for you to fill the map within your 100,000 budget
Easiest ways to keep yourself from going broke (too fast):
When starting off, only use windmills (build them as the demand rises) for power.
When building schools and hospitals, keep funding for them low but keep a close eye on them and adjust every 3 months (sim-time) for the first few years and then every 6 months once the city hits around 10,000 sims. Also keep bussing and ambulance funding at their normal levels unless money gets real tight. Always keep schools covering 98% of your city, this includes high schools and elementary schools, treat each individually. Same goes for hospitals. Within the first few months of your city getting under way, look under your budget screen and if it's available, check to enact the gambling ordinance. If it's not available yet then check back every few months until it is.
Once you get to the point of almost spending all of your 100,000 Simoleans (a lot of the time when you're down to 200-300 or less) you get an offer for the Missile Silo or Military Base. After building at least one of these, your city should be able to make a profit (even if just very small).
In order to keep the number of roads down (less to spend on funding for them), place them before zoning, usually a good rule of thumb is 4 spaces apart and let auto roads place the in between roads.For water towers/pumps, keep them far away from any industrial zones (especially agricultural) and airports/seaports. All industrial pollutes even if just a little bit and can clog your water pipes and they will burst. When placing water pipes, in order to reduce the amount you spend on their funding and maximize their coverage, place them 12 spaces apart except to connect to pumps/towers.
Bridges will not build if you do not have both sides clear of zones/buildings within a few blocks of its starting/ending spot. For roads, there are two main types of bridges, straight across and the "arch" across. Placement of each is dependent of the elevation of its starting point and ending point.
When your city gets to be a decent size, it may be cheaper to build one large police/fire station instead of several smaller ones. Check the coverage and once you get to the point of building the third of either, build a large station to cover your existing city and destroy the small stations. On a medium sized city, you should need 4 large police, fire and hospitals. Also 4-6 high schools on a medium sized map and 9-10 elementary. When building schools and get to your third elementary, also build a small library.
The "rule of 3" is this: your third high school, hospital, police and fire stations should be the large ones. Also starting with your third elementary school, start building a small library next to each. And by the third small library, you should build one main library. Also by the third high school, you should build a college and museum.
On a medium map, this should be about how many of each you should have (if placed effectively):
9-10 elementary, 4-6 high schools, 4 large police, fire and hospitals, 1 college, 1 University, 1 private school, 2-3 places of worship and cemeteries, 1 small airport (replace with medium later if needed)...
After some more play, I'll come back with a couple more tips for you. I have not used trains, highways, or subways yet but I see them as usable only on a large map. Stay tuned! Till then, email me or visit the forums if you have any questions or comments.