The thin tunes, holding lost times and future hopes in liaison, twisted upon the Swiss night. In the lulls of the phonograph a cricket held the scene together with a single note .........

He (Dick) was enough older than Nicole to take pleasure in her youthful vanities and delights, the way she paused fractionally in front of the hall mirror on leaving the restaurant, so that the incorruptible quicksilver could give her back to herself.
He delighted in her stretching out her hands to new octaves now that she found herself beautiful and rich.

1. Use your own composition
This is what for example the French pianist Jacques Lousier has done. He has worked out one improvisation for each piece he plays, then plays it again and again, note for note, at every performance (either from a written transcription or from memory).
There is something to say for this approach when you are a star performer and you have to deliver the goods each and every time, but I personally find it most disappointing. It goes against the spirit and intention of what Jazz is all about.
I had been listening to Lousier's records for years, then 10 or 15 years later I went to one of his live performances in Canberra. He still played every solo exactly the same as on the records we had from him.

2. Improvise following a set series of ideas
This is an interesting idea promoted by the American saxophonist and educator David Liebman.
I became familiar with this approach at a private lesson from one of Liebman's students. You take a blank piece of manuscript paper and write down a series of cameo ideas at appropriate points of the song's chorus.
The idea maybe only one bar in length and can be the start of a phrase, an arpeggio, the beginning of a digital pattern, etc. You may have just one idea for an entire chorus, then another one if you are soloing over a second chorus.   Or you may have different ideas at shorter intervals, say every 8 or 16 bars.
The ideas may not even be all your own either. You may listen to a record or performance by someone else and think "Hey, that is a great idea. I am going to try that too." This happens a lot in Jazz, and is an important mechanism through which it develops an ever expanding vocabulary.
This approach is clearly a good one for quality professional performers. They have their set combination of ideas for a song, ensuring a good standard of performance, while at the same time they can discard it at any instant during their solo if they find they are suddenly on a roll with something new.

3. Have the first phrase in your mind before you start
This is what the well known Australian former ABC arranger, composer and pianist Eric Bryce told me he always does. He mainly does it for the very first song of his performance, just to get off on a good start. Once that is accomplished he is right for the session.
This is more a psychology thing than anything else. Curiously, exactly the same happens when playing contract bridge (or any other sport I imagine). If the first game you play goes well you are right for the evening. But if you make a big mistake, it takes a hell of a long time before you get back on track.

4. Let the mood of the moment inspire you
This is total freedom and of course a lot of fun. The band or backing track, the song itself and the audience (if there is one) set you in a certain mind frame which propels you into your solo. If you play different instruments then the one you play and the technical skill you have over it are also most important.

But be aware, starting an improvised solo is like standing at a road intersection. Which way are you going, North, East, South or West ? The first couple of steps will determine your direction. Likewise the first two or three notes will set the direction and course of your solo.