Begin by creating an account on CoinMarketCap and obtaining an API key. This key is necessary to authenticate your requests and access the cryptocurrency data. Navigate to the API section of your account to create a new API key.

Install necessary programming libraries to interact with the CoinMarketCap API. For Python, you can use the `requests` library to handle HTTP requests. Install it via pip:
```bash
pip install requests
```

Use the API key to make requests to CoinMarketCap's API and fetch the desired data. Here is a basic example using Python:
```python
import requests

api_key = 'your_api_key_here'
url = 'https://pro-api.coinmarketcap.com/v1/cryptocurrency/listings/latest'
headers = {'X-CMC_PRO_API_KEY': api_key}

response = requests.get(url, headers=headers)
data = response.json()
```

Process the fetched data to fit the structure required by Typesense. For instance, you might need to create a list of dictionaries where each dictionary corresponds to a cryptocurrency and its relevant details:
```python
processed_data = []
for item in data['data']:
processed_data.append({
'id': item['id'],
'name': item['name'],
'symbol': item['symbol'],
'price': item['quote']['USD']['price']
})
```

Install Typesense on your server or local environment. You can do this using Docker for quick setup:
```bash
docker run -p 8108:8108 -v/tmp/typesense-data:/data typesense/typesense:0.23.1 --data-dir /data --api-key=xyz
```

Define a schema for your data and create a new collection in Typesense to store the cryptocurrency data. Use the `typesense` client library:
```python
from typesense import Client

client = Client({
'nodes': [{
'host': 'localhost',
'port': '8108',
'protocol': 'http'
}],
'api_key': 'xyz',
'connection_timeout_seconds': 2
})

schema = {
'name': 'cryptocurrencies',
'fields': [
{'name': 'id', 'type': 'int32'},
{'name': 'name', 'type': 'string'},
{'name': 'symbol', 'type': 'string'},
{'name': 'price', 'type': 'float'}
]
}

client.collections.create(schema)
```

Finally, insert the processed data into the Typesense collection. Use the following script to perform the bulk import:
```python
client.collections['cryptocurrencies'].documents.import_(processed_data)
```

By following these steps, you will have successfully moved data from CoinMarketCap to Typesense without relying on third-party connectors or integrations.