Do we have to pay taxes on selling a trailer home if we did not receive a statement from the IRS?

I'm not sure what you mean by "a statement from the IRS". The IRS wouldn't send you a statement for selling your trailer home. 

Yes, you should enter a trailer home, which is a capital asset, on your income tax return. You would only pay taxes on the amount of gain you received. The gain is your proceeds from the sale less your basis in the trailer home. 

• If this is a personal capital asset and you have a loss, you wouldn't be able to deduct the loss. 
• However, if this is a business or rental capital asset,  you could deduct the loss. 

The sale of a personal capital asset is reported as an investment sale. Click here on how to enter it in TurboTax. 

No. The instructions specifically asks you to fill in the number from the form. I did not receive a form

The form you would have gotten is probably a 1099-S.  The 1099-s is only an information form.  The form would have given you the selling price.  If the selling price is lower than the purchase price there will be no tax, but you will not get the benefit of any loss.

@HelenC12 outlined the process perfectly.