Many SWL's find it interesting to send reception reports and to receive QSL's from radio amateurs. But it is far from easy to have success. I think many SWL's should consider some basic facts to improve the quality of their reports. It all depends on the time and effort you are ready to spend on your hobby, but of course success gives more satisfaction!
1. Reports can be written in the form of report cards, similar to QSL cards. However, it is not necessary; sending a letter plus a written presentation or a postcard from your place is a good substitute.
2. Necessary details in the report are:
Your name and address and your SWL call, Receiver and antenna used, Frequency (band) and mode (CW, SSB etc.), Date and UTC time you were listening. QSO info with the RS(T) of the station during each QSO, station called or worked and the report sent in case of the QSO. Also give the signal report for the station in QSO at your end. It is also useful to give callsigns and RS(T) of other stations heard at the same time, especially those in the same country or continent as the station who will receive your report.
3. Reports can be sent via a QSL bureau, via e-mail including eQSL and direct.
I often combine an e-mail report in letter form with a SWL card via the bureau. If the station is rare or writes in QRZ.com that he/she will only reply to direct mail, the report must be sent direct, of course. In case of DX'peditions you have to include an International Reply Coupon or 1-2 US dollars to cover to expense for a reply. This can be quite expensive, so you better think twice.
Now some more comments:
I highly recommend spending some time on the reports. You should write so that the radio amateur finds your report valuable or at least nice to read. A personal presentation with some photo is quite helpful. Be personal, show the radio amateur that you got something out of your listening to his QSO's! Never send a report on just a CQ! And only one QSO given, without the signal report sent, can raise suspicion that you have copied his callsign from a DX cluster (in case this is a very rare call-sign). If you hear the same station on different bands, he will be interested in your report. I have the San Marino station T77C confirmed on four different bands.
I think this covers most of important points in sending reception reports. I wish all those who engage in this interesting part of our hobby the best of luck!