My first game I quite happily built away for about 100 turns, then the Divine Ascension declared war on me and literally wiped out 3 of my cities and 75% of my units in several turns with nukes... the AI can be absolutely ruthless if it gets ahead of you.
Here's my early game strategy, hopefully some of it helps!
Going for Colonization Fervor as early as possible usually seems to be a good idea. Ideally don't have any farmers and only enough miners & workers to build 2-3 units for exploration and put everyone else into science. With the free colonizer you can build your second city near resources you need, with minerals being top priority - e.g. if your first city has an observatory and no mountains your second city needs a mineral special resource and/or mountains. Food bonuses can wait til your 3rd city.
The 2-3 units should be grabbing every ruin they can, the free resources are very helpful. They should travel far and not expect to make it home, just to get lots and lots of ruins.
Then when you have a few flame troopers, go get nearby hives as per the link willgamer posted
Keeping your tax rate low helps a little too, 35% max for young cities, basically just enough to fund your army (unless you're Noxium which justifies higher taxes).
I usually build extra cities early on only to get needed resources. My ideal early-game cities would be 1) military production city (ideally with Xenite flowers) 2) science city (with observatory) 3) minerals city (with mountains) 4) food city (special resource & grassland). In practice 3-5 cities usually gives the right balance because most cities will have 2 specialisations. More than 5 cities and you have to build a lot more buildings to get the bonuses, less and you're definitely missing out on special resources. You'll want to build or buy the bonus buildings for each city's specialisation asap, starting with refining arrays.
Specialising means you get the same bonuses more quickly from fewer buildings, so is better than having all-rounder cities. A food or minerals specialist city will have to become something else when it outgrows the terrain but a Science or Production city can have 100% scientists or workers for most of the game.
Minerals are the key resource so mountains are the best terrain to grab, you don't need a lot of grassland area because you only need enough food - but you can always use more military units, operations etc, all made from minerals. Similarly you should beeline mineral-increasing techs and get those buildings as quickly as possible. I also like morale-boosting buildings, stock markets, science basically anything that increases production, credits or tech. Food bonuses I get if I'm running low on food.
In terms of military I usually have the production-focussed city (often the capital) with 70-100% workers churning out units for pretty much all the early game, which is enough to hold off the AI on Very Hard. If your military is on par or only slightly behind they stay on good terms with you so it's vital to build a lot of units, even if you do nothing with them.
Also Solar Dynasty is probably the easiest faction to start with (just build lots of forests to cut pollution!) and Togra/Imperium/Terra Selvum can be harder.