DGers are often willing to share their extra seeds without a trade in return. Some "seeds for postage" offers are for seeds collected in huge quantities or are made at the end of the season to clear out the seed box. Other people enjoy sharing seeds with new gardeners, often paying forward somebody else's generosity. Maybe you tried to arrange a trade, and the person didn't need anything you had but was still willing to share. Whatever the reason for the offer, a few tips on how to respond will make it easier and more fun for everybody.
Put your best foot forward. Read the Trading Primer for some good tips on trading etiquette. If the "seeds for postage" offer asks for requests to be posted on the thread, don't send Dmail instead. Dmailed responses can be harder to keep up with, and your request might be misplaced. Remember that you're not placing an order with a catalog, you're responding to somebody offering to do you a favor. Use phrases like "if these seeds are still available, I would like..." and words like "please" and "thank you." Send postage promptly.
Ask only for seeds you intend to grow. It's bad form to jump on SASBE offers and then trade the seeds away, and you'll end up with a reputation you don't want. It's easy to get swept up in the moment. Pause to look up plants in Plant Files. If you don't think you'll be able to start the seed, or if you have no place for the plant in your garden, then let somebody else have it.
You'll often see the acronyms SASE and SASBE -- Self Addressed Stamped Envelope and Self Addressed Stamped Bubble Envelope. Mostly, people ask for SASBE, so seeds will be protected in the mail. This doesn't literally mean you need to put your address and stamps on a bubble envelope and then enclose it in another envelope in order to send it. There's an easier way!
I've sent and received many SASBEs since joining DG. Here is what I include or what I ask for when somebody is sending me a SASBE.
1. A bubble envelope, addressed to the person offering the seeds, with sufficient postage to get it there. Bubble envelopes need extra postage to cover the USPS "nonmachinable surcharge." You don't want your SASBE to arrive with postage due! See the USPS Customer's Guide to Mailing for current postage rates. Put your return address on the envelope also, including your Dave's Garden (DG) name.
If you are having trouble coming up with a BE, ask if your trader would be willing to provide one if you send an extra couple of stamps. Bubble envelopes can be re-used.
2. An address label with your address on it. This will be placed on the outside of the bubble envelope when it is returned to you, so please make sure it's large enough to cover the outgoing address. Again, it's helpful to note your DG name on this label.
3. A note with your DG name, listing the seed(s) you are requesting. Including this information is important! Without it, I have no way of knowing that "Sally McPherson from Idaho" is "PinkFrogLady" who desperately wanted ‘Spicy Orange Australian' Basil seeds. 
4. Enough loose postage to cover the return of the envelope with the seeds. Do not send a pre-paid metered label, as the postal service won't accept them. Often, traders will tell you how many stamps to send. If not, consider that seeds may be heavy or bulky enough that the envelope may have to be posted as a "small parcel" on its return. The USPS Domestic Mail Manual has complete information on rates, fees, and regulations.
International DGers don't need U.S. postage stamps in order to share seeds with U.S. members (or vice versa). That's what an International Reply Coupon (IRC) is for!  Please check with your sender before using IRCs. Since a BE full of seeds is bigger than a standard airmail letter requiring one IRC, you'll need to ask the other country's postal administration how many will be needed. Check the USPS International Mail Manual (372.3b) for current IRC exchange rates. Also, look up the import and export regulations of both countries.
Seed giveaways are one of the special things DGers do for each other. I appreciate the effort that goes into collecting, de-chaffing, and packing seeds. Especially when responding to an offer of seeds for postage, I want to do everything I can to make sending the seed as easy as possible. Reading the offer carefully and being sure to include sufficient postage and all necessary information (including your DG name!) definitely helps.
The next time a phrase like "seeds for postage" or "SASBE offer" catches your eye, check it out!
Photos in this article are of plants often mentioned in "seeds for SASBE" offers. Moving your mouse over the photo will pop up a caption with the name of the plant.
 This is a completely fictitious example. I don't have any ‘Spicy Orange Australian' Basil seeds. And "PinkFrogLady" isn't (currently) a DG username.
 Thanks to KennedyH for reminding me about IRCs and for explaining them to me so well.