Here's a strategy for writing melodies that I've used with good results. What I do is, instead of taking some lyrics and writing music for them, I just pick a book at random and write music for a chunk of the text.

Starting Out

I choose an existing song with a "feel" I'd like to create in a new song. (There's a good online resource of songs from the past at everyHit.com: they have a retro-chart featuring every song that's been a hit in the UK.)

I will run the first line - or a few lines - of the chosen song (I'll call it the foundation song) through my head to get into the "feel" of the song, and then I'll aim to make the next line of the song a completely new melody, but still with the same feel as the foundation song.

I create this melody by reading a line from the text in a book, but instead of reading it in the normal rhythm of reading, I sing/read the line so that it has a similar rhythm to that of the foundation song. As I sing/read I make sure that I create a new melody as I go. From that line I move on to the next line, singing/reading the line with a new melody. The structure of the words in the sentence should help to force me to create new rhythms, which in turn helps in the creation of a new melody.

Dividing the line of text, pitch of notes, and direction of notes:

Dividing the line of text

When sing/reading a line of text I sometimes divide the line into sections. So, if I divide the following text:

We walked into the cave and felt unnerved by the eerie silence.

into two sections:

We walked into the cave and // felt unnerved by the eerie silence.

I'll treat each of the sections as a whole idea in its own right - that is, the first section (we walked into the cave and) will be one line of a verse (or chorus) and the next section (felt unnerved by the eerie silence) will be the next line of verse or chorus. I pause between the sections (represented above by "//").

I can also divide a line into three parts:

We walked into the // cave and felt unnerved // by the eerie silence.

again with each section being an idea in its own right and the "//" being a pause.

Or I can treat the whole line as a whole idea:

We walked into the cave and felt unnerved by the eerie silence.

Choosing the pitch of notes

When I'm about to sing/read a line of text, I choose the starting pitch of the starting note (or notes). My starting note(s) will either be higher, lower, or about the same as the last note of the previous line. I don't follow this rule religiously -- I don't worry about using a keyboard to make sure the note is correct. It's just a rough guide.

Note direction

I also decide the direction of the notes in the next line I'm about to sing/read. The direction can be:

Ascending

About the same

Descending

Again, I don't follow this rule religiously or expect every single note to follow the direction chosen.

Pause

The "//" sign on the line of text used above denotes a pause. Sometimes I will pause by making a count before proceeding on to the next line of the song. To do this I decide on how many beats will make up my pause - it's usually from one beat to seven. The tempo of the count is the same as that as the song.

One further point:

I don't select a chunk of text from a book and use that as a set lyric as though I have to write a good tune for that chunk of text -- I keep proceeding through the book, taking different chunks of text for my verse and chorus etc. I like to think that the slight differences in rhythms created by using different words can make the difference between a melody being ordinary or being a really strong hook.