You were invited to set up Siri when you first set up your iPhone or iPad. If you did this, the default settings may not be the best for blind and low vision users. I suggest you review your Siri settings and take a look at Suggested iPhone and iPad Siri settings. If you haven't already done the initial setting up of Siri, you'll find instructions in that link.
The main Siri settings are in Settings / Siri or Settings / Apple Intelligence & Siri if your device supports Apple Intelligence. From here on I'll use "Apple Intelligence & Siri" to stand for both. Some additional settings can be found in Settings / Accessibility / Siri. The settings in Accessibility / Siri include one to change Siri's speaking rate between 80% and 200% of its normal speaking rate which may be helpful if you either need more time to process Siri's responses or if you like to get things done quickly with speeded-up voices.
Another setting in the Accessibility Siri settings is Siri Pause Time. This can be helpful if you tend to hesitate while speaking instructions to Siri and Siri jumps in with it's response before you have finished. You can increase the pause time to either "longer" or "longest". There is a more robust way to avoid Siri responding before you have finished your instruction which is described below in the section headed "keep Siri listening with a long button press".
Siri can be activated with two spoken commands, "Hey Siri" or "Siri". There is a setting in Settings / Apple Intelligence & Siri which allows you to choose whether Siri listens for both "Hey Siri" and "Siri" or just for "Hey Siri". To avoid making this text too clumsy, I'll use "Hey Siri" to mean "Hey Siri" or "Siri". The choice to listen for Siri or Hey Siri may not be available on some iPhones or iPads.
To give Siri an instruction or ask a question speak "Hey Siri" followed immediately by the command or question. An example would be to speak "Hey Siri text John Smith I'm on my way". If Siri needs more information from you, it will request that information. Speak your response after Siri finishes speaking and makes a sound or haptic buzz to let you know it is listening.
After Siri has responded to your first instruction you can give additional instructions to Siri without the "Hey Siri" prefix so long as you don't wait too long. You can even interrupt Siri with a new command. This feature may not be available on all iPhone or iPad models and can sometimes be a little unreliable.
When you no longer require Siri it can always be dismissed with the spoken command "hey Siri goodbye". Alternatively, Siri can be dismissed with a brief click of the Home, Side or Top button, depending on your device. Note that Siri is automatically dismissed when it has opened an app.
As an alternative to speaking "Hey Siri" to activate Siri, Siri may be activated using a button press on all iPhones and iPads. If your device has a home button, then that is the one to use. If your device has no home button then use the Side button on iPhones or the top button on iPads. For brevity, I'll just refer to this as "the button". To activate Siri, hold down the button until you hear a sound or feel a haptic vibration and then release the button and speak your instruction and wait until Siri responds. If Siri requests more information be sure to wait for it to finish speaking and play its sound and buzz before answering.
Dismiss Siri with a brief button click.
For some people, even if the Siri Pause Time is set to longest, Siri may still jump in and deal with incomplete instructions if they hesitate. It's possible to ensure that Siri continues listening until you have finished speaking. Hold down the button until you hear the sound or feel the haptic buzz, but now continue to hold the button down while you speak your instruction. Lift your finger only when you have finished speaking your instruction.