What are some examples of warning areas and restricted areas?
I'll provide information for the US airspace. However many countries, ICAO members, will have similar concepts and procedures.

Short answer

You are not required to follow any procedure for entering a warning area or an inactive restricted airspace. In the latter case, you need to ensure the area is actually inactive. A safe practice is to contact the controlling agency of the area prior to enter any warning or restricted one.

The longer answer below develops a bit around special use airspaces which encompass warning and restricted airspaces among other. You'll also find two examples of these areas.



Context

The airspace over the US is open to navigation, a part of this airspace benefit from services provided by air traffic control (ATC), e.g. safe separation and traffic information.

This controlled airspace includes airport areas and airways, and other areas of interest. It is is ruled by air regulations relative to airspace classes. In the US these regulations are found in document 94 CFR 91.


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Some limited areas, that may be permanent or temporary, can be prohibited or restricted. Together they constitute the special use airspaces (SUA)



Special use airspaces

SUA (Wikipedia):


  Special use airspace includes: restricted airspace, prohibited
  airspace, military operations areas (MOA), warning areas, alert areas,
  temporary flight restriction (TFR), national security areas, and
  controlled firing areas.


The SUA are repertoried by the FAA: SUA Web site.

You may search by name or scan the map. R denotes a restricted airspace, and W a warning area.





More on SUA: Course Notes, Dennis Seals, FAA

Your question is limited to warning areas and restricted airspace.



Restricted airspace

Wikipedia:


  Restricted areas denote the existence of unusual, often invisible,
  hazards to aircraft such as artillery firing, aerial gunnery, or
  guided missiles. Penetration of restricted areas without authorization
  from the using or controlling agency may be extremely hazardous to the
  aircraft and its occupants.


See also chapter 3−4−3. Restricted Areas of the FAA-AIM.

Entry: Forbidden when active, subject to ATC clearance on a case by case basis.

For areas that have a scheduled activity, times of activation are published in the AIP. When inactive, a R-area is just a like any other location of the surrounding airspace class. When active it is just forbidden to enter it (albeit FAA may deliver specific clearances if solicited).

For VFR flights, contacting ATC prior to entering an inactive restricted area is not mandatory per regulations, but is a good practice regarding safety. IFR flights under monitoring of the ATC, will not be authorized to enter an active restricted area.

Wikipedia:


  Restricted airspace zones may not be active at all times; in such
  cases there are typically schedules of local dates and times available
  to aviators specifying when the zone is active, and at other times,
  the airspace is subject to normal VFR/IFR operation for the applicable
  airspace class.


Activity time may happen unscheduled for some R-areas. A schedule cannot be published, in this case a NOTAM is used to inform airspace users.

Wikipedia:


  A few zones are activated by NOTAM; an example is R-2503D over Camp
  Pendleton in southern California, between San Diego and Los Angeles.
  This particular zone, beginning at 2000ft above sea level over most of
  southern Camp Pendleton, can only be active for a certain number of
  days per year, thus allowing small planes to fly a direct route over
  land between the two metro areas instead of being diverted offshore or
  into mountainous terrain further inland.


Example: Restricted areas R-2501 around the Twentynine Palms Marine Corps Air Ground Combat Center:



GlobalSecurity.org:


  The Twentynine Palms Complex is located in the Southern California
  desert approximately 115 NMI northeast of Los Angeles, CA. The
  Twentynine Palms Complex provides a vast land and restricted airspace
  (R-2501) area for live ordnance employment and combined arms training
  of infantry units, armored vehicles, artillery, and air support.
  
  The complex includes the following instrumented area: R-2501E
  
  The following are training, and Military Operating Areas (MOAs)
  associated with the Twentynine Palms complex:
  
  
  R-2501N
  R-2501W
  R-2501S
  Bristol MOA
  Sundance MOA
  Range Training Areas (RTA)
  


Description of R-2501N from Order JO 7400.8S:

R-2501N Bullion Mountains North, CA 
Boundaries.
Beginning at lat. 34°30'00"N., lon g. 116°26'23"W.;
to lat. 34°36'00"N., long. 116°28'03"W.;
to lat. 34°40'30"N., long. 116°29'43"W.;
to lat. 34°43'00"N., [...]
Designated altitudes. Unlimited.
Time of designation. Continuous.
Controlling agency. FAA, Los Angeles ARTCC.
Using agency. Commanding General, Marine Corps Base, Twentynine Palms, CA.


This area around a large military complex is active (restricted) 24x7, at any altitude. A pilot who wants to enter this area for some reason needs to contact either the controlling agency (Los Angeles ARTCC) or the using agency (Marine Corps Base).



Warning area

Chapter 3−4−4. Warning Areas of the FAA-AIM.


  A warning area is airspace of defined dimensions, extending  from
  three nautical miles outward from the coast of the U.S., that contains
  activity that may be hazardous to nonparticipating aircraft. The
  purpose of such warning areas is to warn nonparticipating pilots  of
  the potential danger. A warning area may be located  over domestic or
  international waters or both.


Entry without specific clearance, but can be hazardous. Contacting ATC prior to entering a warning area is not mandatory per regulations, but is a good practice regarding safety.

Example: Pacific Missile Range Facility (PMRF) NS Barking Sands.



GlobalSecurity.org:


  The area surrounding Kauai is divided into warning areas with W-186
  and W-188 controlled by PMRF. The Fleet Area Control and Surveillance
  Facility (FACSFAC) controls W-187, 189, and 190. Space, air, and
  surface tracking are accomplished from PMRF precision-tracking radar
  sites at elevations of 75 ft., 1700 ft., and 3800 ft. These are
  supported by radar systems operated by agencies external to PMRF.


Description of W-188 from Order JO 7400.8S:

W-188 Hawaii, HI 
Boundaries. Beginning at lat. 21°58'19"N., long. 159°48'45"W.;
to lat. 21°58'27"N., long. 159°59'50"W.; [...]
Altitudes. Surface to unlimited. 
Times of use. Continuous. 
Controlling agency. FAA, FAA, Honolulu Control Facility. 
Using agency. Commander, Pacific Missile Range Facility, HI. 




More:


Related question: Can a pilot fly through a restricted area while flying on a Victor Airway?