Here's a basic CSS file to style your simple to-do list web app:

```css
/* Basic reset */
* {
  margin: 0;
  padding: 0;
  box-sizing: border-box;
}

body {
  font-family: Arial, sans-serif;
  background-color: #f4f4f9;
  display: flex;
  justify-content: center;
  align-items: center;
  min-height: 100vh;
}

.container {
  background-color: #fff;
  width: 100%;
  max-width: 400px;
  padding: 20px;
  box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);
  border-radius: 8px;
}

h1 {
  font-size: 24px;
  margin-bottom: 20px;
  text-align: center;
  color: #333;
}

form {
  display: flex;
  margin-bottom: 20px;
}

input[type="text"] {
  flex: 1;
  padding: 10px;
  font-size: 16px;
  border: 1px solid #ddd;
  border-radius: 4px;
}

button {
  padding: 10px 15px;
  margin-left: 10px;
  background-color: #28a745;
  color: #fff;
  border: none;
  border-radius: 4px;
  cursor: pointer;
  font-size: 16px;
  transition: background-color 0.3s;
}

button:hover {
  background-color: #218838;
}

ul {
  list-style: none;
}

li {
  padding: 10px;
  background-color: #f9f9f9;
  border-bottom: 1px solid #ddd;
  display: flex;
  justify-content: space-between;
  align-items: center;
}

li:last-child {
  border-bottom: none;
}

.task-text {
  flex: 1;
}

.remove-btn {
  background-color: #dc3545;
  color: #fff;
  border: none;
  border-radius: 4px;
  padding: 5px 10px;
  cursor: pointer;
  font-size: 14px;
  transition: background-color 0.3s;
}

.remove-btn:hover {
  background-color: #c82333;
}
```

This CSS file provides a clean and simple design for your to-do list app. It includes styling for the layout, buttons, and task items, as well as hover effects for better user interaction. Feel free to customize the colors and styles to fit your preferences.