The biggest advantage Spawn have against Marines are inexperienced players and fear. The biggest disadvantage Marines have against spawn is spawn friendly terrain. See Assembling A Fire Team for how to keep your resources organized.
I make sure when I deploy I can generally fall back to a well defended area, preferably with plenty of low cover to make drones do plenty of work to get to my forces. Keep an HQ nearby or deploy two of them so you can keep your perimeter quickly
Clear any terrain out of the way that could provide cover for spawn with commanders and naders, get to see them sooner, especially those pesky splatters.
Grenadiers lay down a denial of movement barrage for the spawn, keep those 'naders firing, they're no good in close quarters, if you don't hit your spawn at maximum range they're drone/buzzer meat. Use the short bounce tactic to bounce the grenades high. Assemble a Fire Team of Grenadiers able to move into contact and lay down crushing short bounces.
Snipers are great for spotting and maybe taking out a distance unit, but only if you have a good view, otherwise use for leveling terrain and scouting. The farther you see the Spawn Rush, the better you can target it and move your men into formation.
Medics should be fighting more than healing. 10 shots into the enemy is worth much more than healing a single unit by a few points. In between waves of spawn heal your grunts first then commanders, snipers and grenadiers, which can be used as spawn bait to save the real fighters.
Group your shooters so they can give curtains of fire. See Fields_of_Fire
Cover windows by a number of units for buzzer attacks.
Look at the terrain and consider what paths the enemy will have to take, cover those. Try denying the paths with withering counter fire and Grenadier area effect. See Denial Of Area for the concept.
Depending on how it goes your next problem is going to be running out of ammo. So make sure the HQ is in an easy-to-supply-your-forces place.
Don't be afraid of sacrificing men, it's likely some will die, if you lose a few don't think you've lost, just rearrange your forces. You will lose less if you follow Mutual Element Support.
(Thanks to Dillinja)
Marine vs Spawn generalities I keep in mind.
When moving troops some run for 5-7 seconds and then stop to allow defensive fire. Others OpFire for 4 sec or so then run to catch up. Maybe 1 or 2, maybe, will be on Halt On Sight.
Grenadiers are in front of the other troops whenever possible. Their range is thus extended, they are sturdier than any Marine except the Commander and they are the perfect chewtoy to drag the rush past your shooters or to be a suicide bomber if they are doomed.
All troops reload whenever possible, generally when 25% or even less ammo has been expended. When the rush hits, it's too late to reload.
Wounded troops, no matter how slight, are ASAP gang healed by the multiple medics you of course brought. When the rush hits, it's too late to heal and your Medics become frontline troops. See Safe House Team under Assembling A Fire Team.
Denial of resources - queen laying eggs. Naders will throw an extra nade whenever possible to blow up the bodies of those they just killed to deny recycling.
Breaching / Wallbusting: Snipers and Commanders can be used to punch holes through terrain to allow buildups to be spotted. Only every other spot should be shot out to slow up Queens and rushes while allowing nades free access.
Versus Buzzers, only close range shots matter. If Buzzers are weaving about on ammo wasting duties, have your units hold fire or simply run away and back for about the time it would take them to reach you if they rushed you.
Point count. You need to know.
(Thanks to Indricotherium)
There are a lot of rookie players who go straight to Spawn after watching the devastation it can wreak on unorganized jarheads. By keeping your element / fire team discipline and scouting out a defensive area upon drop, you can survive and win. See Defensive Warfare and Defense In Sector for specifics.