Okay, so as someone who suffers from heartburn both when I'm preggers and when I'm not, I feel like I should weigh in here and share what I've learned over the years...
First of all, yes, greasy, fatty, spicy, sugary foods make it worse, but when you're pregnant that's almost irrelevant because everything makes you have it. I believe this is mainly because your body produces a hormone called relaxin when you're pregnant and it helps to relax your hip joints so you can open up to have the baby... it unfortunately also relaxes all of the sphincters in your body. Therefore, we get the lovely bonuses of hemerroids and indigestion! (Some lucky people do have the fun bonus of getting really flexible in all their joints while they're preggers, but I'm not one of those.)
Here are the things I have found the most helpful in dealing:
1) Learn to meditate... I just started trying this method with this pregnancy and it (amazingly) helps a whole lot. Here's what I mean - focus on your breath for a little bit, then start to notice the feeling (for me it's an intensely burning esophagus, and just notice it. Don't judge it as being bad, just make note of every little thing about it. Some how, it makes it not quite so terrible.
2) Papaya enzymes!!! I eat them 3 at a time, as often as I need them.
3) Slippery Elm Bark lozenges. I made my own by mixing slippery elm bark powder with a little bit of honey (until it makes a dough consistency), then rolling it into thin "snakes" and cutting it into 1/2 inch lozenges. Bake them on parchment paper at 250 for about 10-15 minutes. Viola! Homemade relief!
4) Liquid Calcium Magnesium seemed to help me a LOT last time, but I haven't used it yet this time.
5) A handful of raw almonds seems to help a bit if it's not really extreme indigestion.
6) I've also found that a cup of mama tea with some milk and honey in it seems to help a lot too. I like to make a pot and have a cup hot, then put the rest in the fridge to drink cold later (I still like to put milk and honey in it).
Hope some of these tips are helpful... I guess another really good one to remember is "this too shall pass".
Happy indigestion battling!