I don't have a replay handy, but I will give you a set of instructions. As John Connor said in The Teriminator, "Do what I say! Do exactly what I say! Don't make a move unless I say! Don't make a sound unless I say! Do you understand? DO YOU UNDERSTAND?!?"
Follow these instructions and you will win. Note that these are not instructions on how to enjoy the game - you can figure out how to do that on your own later. These are simply instructions on how to win, since that seems to be what you are having trouble doing.
1) Select small random map. Normal difficulty. ALL SPEEDS NORMAL OR BELOW. Pirates off. Normal start. Normal fleet size.
2) Select TEC or Vasari as your race, because the unit build I'm going to give to you is easier to achieve with those factions.
From here on out, note that THERE IS NO TIME DELAY OR DICKING AROUND WITH ANYTHING, PERIOD. When the game starts, you start moving on these instructions. The only time there should be a delay is if you are waiting on resources - that's it. Make sure you know how to use the black market to buy/sell metal/crystal. Also, understand that as soon as you take an asteroid, upgrade planet population one time. All other planets you take, you will upgrade planet population two times. Again, you don't dick around to do this (or anything else), YOU DO IT AS SOON AS THE PLANET IS COLONIZED.
3) Game starts. Sell 200 metal. Build at least 1 scout per phase lane leading out of your homeworld (a minimum of 3). Set scouts to autoscout by right clicking on autoscout.
4) Build capital ship factory. Queue up the colonizing capship.
5) Build 1 colony frigate.
6) Build 1 military lab if you are vasari, or 2 military labs if you are tec.
CHECKPOINT: 3-6 should have taken you around 10 seconds to queue up. If it didn't, you did it wrong, so quit the game and do it again (and again, and again). Note that I'm not saying the structures and capship should be finished within 10 seconds. I'm saying they should all be queued up and building (note that you don't need the capship factory fully built to queue up a capship - you can queue it up as soon as the factory starts building).
7) Research lrf (long range missle frigate) if you are TEC, or assailant if you are vasari. Of course, if you need crystal, buy it. You don't need to wait for your labs to finish building - go ahead and queue up the research.
8) As soon as a scout uncovers the asteroid which should be connected to your homeworld, send your colony frigate ALONE to take it (if there is no asteroid connected to your homeworld, quit the game and restart it). As soon as the colony frigate jumps to the asteroid, colonize it (buying metal/crystal if necessary), then build a turret as close as you can to the asteroid, while at the same time being as close as possible to the siege frigate firing at the planet. If you do this correctly, the siege frigate's bombs should be passing through the turret. If this is happening, you know it is in the correct location. Retreat with your colony frigate - the turret should kill the militia. Upgrade planet population, queue up all extractors. If you lose the colony, you did this entire thing wrong.
CHECKPOINT: All of 8 should be accomplished within 20 seconds or so of your frigate arriving to the asteroid. In other words, the roid should be colonized, the population upgrading, the turret building, the extractors building, and the frigate retreating. If it takes you appreciably longer, you are doing something wrong, so do it again (and again, and again).
9) Mash "build lrf" or "build assailant" over and over again until either funds run out, or you've built so many that you've reached your population cap. When your fleet cap has been reached, research the next upgrade for fleet cap, and mash "build lrf/assailant" more. Never stop mashing that button for long. You should never have money laying around not being spent. If your money isn't being spent on labs, research, upgrading colonies, or upgrading your fleet cap, it should be spent mashing that "build lrf/assailant" button over and over again. If you have money, metal, or crystal just laying around, you are doing something wrong.
10) Send capship to nearest asterioid, terran, or desert planet your scouts uncover (but NOT the roid you sent the colony frig to). If there isn't a terran, desert, or asteroid around, then send it to the nearest ice or volcano. Kill the siege frigates guarding the planet with your capship, colonize the planet (if terran or desert or asteroid), upgrade population, then drop 1 or more turrets next to your capship, depending on the severity of militia there. Queue all extractors, kill all militia, move to next nearest planet, rinse, repeat. Never stop this capship from moving. It should either be en route to a planet, fighting at a planet, colonizing a planet, or possibly repairing itself somewhere. If you had to send the capship to a vlocano or ice, just kill eveything there and move on. You can't currently colonize that type planet yet.
11) If vasari, when funds permit drop 1 civ lab at your homeworld and 1 civ lab at your asteroid. If tec, upgrade the logistics at your asteroid and drop 2 civ labs there. Research either ice, volcano, or both, depending on what you have near your homeworld.
12) You never stopped building your lrf/assailants, right? Send that fleet of assailants/lrf at your homeworld to meet your capship. If your capship had to skip planets, just kill everything at those planets on the way to your capship. Send your colony frig to any nearby volcano/ice worlds that have been cleared, and colonize, remembering to upgrade planet population twice, and build all extractors. Select your homeworld at this point, and set the rally point of that planet to be your capship itself. For the rest of the game, remember to keep mashing "build lrf/assailant," upgrading your fleet capacity when necessary.
13) Just keep on colonizing, moving towards the general direction of your enemy. When you see an enemy planet, attack it with your entire fleet. Kill everything there, bomb the planet, take it, then move on to the next one. If you lose your capship, build another one so that you can continue bombing planets and colonizing them.
You should have won the game, rather easily.