Wav2Prompt is proposed which allows straightforward integration between spoken input and a text-based large language model (LLM). Wav2Prompt uses a simple training process with only the same data used to train an automatic speech recognition (ASR) model. After training, Wav2Prompt learns continuous representations from speech and uses them as LLM prompts. To avoid task over-fitting issues found in prior work and preserve the emergent abilities of LLMs, Wav2Prompt takes LLM token embeddings as the training targets and utilises a continuous integrate-and-fire mechanism for explicit speech-text alignment. Therefore, a Wav2Prompt-LLM combination can be applied to zero-shot spoken language tasks such as speech translation (ST), speech understanding (SLU), speech question answering (SQA) and spoken-query-based QA (SQQA). It is shown that for these zero-shot tasks, Wav2Prompt performs similarly to an ASR-LLM cascade and better than recent prior work. If relatively small amounts of task-specific paired data are available in few-shot scenarios, the Wav2Prompt-LLM combination can be end-to-end (E2E) fine-tuned. The Wav2Prompt-LLM combination then yields greatly improved results relative to an ASR-LLM cascade for the above tasks. For instance, for English-French ST with the BLOOMZ-7B1 LLM, a Wav2Prompt-LLM combination gave a 8.5 BLEU point increase over an ASR-LLM cascade.