Insulating a shed economically involves a mix of resourcefulness and effective use of available materials. Here are some of the cheapest or free ways to insulate your shed:

1. **Bubble Wrap**: This is a cost-effective method, especially for small sheds. You can often find large rolls of bubble wrap at low cost or even free from local stores or online marketplaces where people are looking to dispose of packing materials. Attach the bubble wrap to the walls of the shed using staples or strong adhesive tape, and ensure that the bubbles face inward to trap air effectively.

2. **Recycled Foam Boards**: Scour construction sites, online giveaways, or recycling centers for used or surplus foam insulation boards. These can be cut to fit the spaces between the structural framing of your shed. Ensure any gaps are sealed using caulk or foam spray to enhance the insulative properties.

3. **Fiberglass Batts**: While not free, fiberglass insulation is often one of the cheaper options available at home improvement stores. Sometimes, you can find off-cuts or second-hand rolls sold at reduced prices. It’s effective and can be installed between framing easily, but you’ll need to wear protective clothing as fiberglass can irritate the skin and lungs.

4. **Repurposed Polystyrene**: Look for used polystyrene sheets from product packaging or old appliance packaging. Polystyrene can be cut to fit the walls, ceiling, and even the floor of your shed, providing a reasonable insulation layer.

5. **Cardboard**: Layers of cardboard can serve as an insulating material, especially when combined with other insulating materials. Cardboard is readily available and can be free. Stack multiple layers or create a cardboard sandwich with other materials like bubble wrap or polystyrene for better insulation.

6. **Old Carpets or Rugs**: Carpets and rugs can be used to insulate the floor or walls of your shed. These are often available for free or cheaply from local disposal groups or when people clear out old furnishings. They can add a layer of warmth underfoot and help prevent heat loss.

7. **Wool or Cotton Clothing**: Old wool sweaters or cotton batts can be repurposed as insulation. This method is particularly sustainable and can utilize clothes that are too worn for donation. Compress these materials into cavities in walls or ceilings for a makeshift insulation solution.

8. **DIY Straw Bales**: If you have access to straw bales, they can be a very cheap insulation solution. Straw has excellent insulating properties and is commonly used in eco-building projects. Just make sure that the straw is dry and remains dry to avoid issues with mold or rodents.

When using any type of insulation, it’s crucial to also consider moisture control. Ensure that there’s a vapor barrier or sufficient ventilation to prevent condensation, which can lead to mold and damp issues.