Your situation
The offer is a conclusion. Ask for the reasoning.
An offer is one number produced by one appraisal commissioned by the party buying. The appraisal behind it contains every judgement that produced that number, and that is the document worth reading.
The one thing to do first
Ask for the complete appraisal, in writing
Agencies frequently send a one page summary with the offer. That is not the appraisal. Ask for the full report, in writing, and keep a copy of the request.
In acquisitions with federal funding the agency must provide a written statement of the basis for the offer, which in substance means the appraisal. Many states impose a similar duty. A refusal is unusual and it does not help the agency later.
Without the report there is nothing to examine. With it, most owners can tell within an afternoon whether the reasoning is thorough or thin.
Signals
What suggests the offer deserves a closer look
No before value and after value
If part of your property is being taken and the report does not value the remainder separately, the method that captures damage was not applied.
Severance damages stated as none
A conclusion of zero needs reasoning like any other number. Its absence is a gap, not a finding.
Current use assumed throughout
Sometimes correct and often convenient. Look for whether any alternative use was considered.
A rate per square foot
Reasonable for the land, and it cannot capture what the taking did to the rest of the property.
Fixtures and planting not itemised
Fences, paving, wells, septic and mature trees contribute to value and are routinely left out.
Nothing for temporary areas
Construction areas are a separate compensable interest, not a free margin.
Questions about offers
The offer expires in two weeks
Most such dates are soft. An agency that needs your property will keep talking. Ask for the position in writing rather than acting on a verbal warning.
Will they reduce the offer if I negotiate
In practice no, and in federally assisted acquisitions the offer may not be less than the approved appraisal figure.
Should I just accept it
Sometimes that is right, particularly for a small taking with a well reasoned appraisal behind it. Read the reasoning first, because once you sign, the matter is closed.
The detailed answer
Reading an offer, testing it and deciding is covered in depth at Reading the offer.
Find the site that answers your question properly
This is a starting point. The detailed answers live on the sites built for each question, and on the site for your state.