como puedo realizar alertas en primefaces

Puedes usar bien los dialog, los growl o los message.

Dialogos

<h:panelGrid columns="1" cellpadding="5">
    <p:commandButton value="Basic" type="button" onclick="PF('dlg1').show();" />
 
    <p:commandButton value="Modal" type="button" onclick="PF('dlg2').show();" />
 
    <p:commandButton value="Effects" type="button" onclick="PF('dlg3').show();" /> 
</h:panelGrid>
 
<p:dialog header="Basic Dialog" widgetVar="dlg1" minHeight="40">
    <h:outputText value="Resistance to PrimeFaces is futile!" />
</p:dialog>
 
<p:dialog header="Modal Dialog" widgetVar="dlg2" modal="true" height="100">
    <h:outputText value="This is a Modal Dialog." />
</p:dialog>   
 
<p:dialog header="Effects" widgetVar="dlg3" showEffect="explode" hideEffect="bounce" height="100">
    <h:outputText value="This dialog has nice effects." />
</p:dialog>

Growl

<h:form> 
    <p:growl id="growl" showDetail="true" sticky="true" />  
 
    <p:panel header="Growl">  
        <h:panelGrid columns="2" cellpadding="5">  
            <p:outputLabel for="msg" value="Message:" />   
            <p:inputText id="msg" value="#{growlView.message}" required="true" />  
        </h:panelGrid>  
 
        <p:commandButton value="Save" actionListener="#{growlView.saveMessage}" update="growl" />  
    </p:panel> 
</h:form>  

Growl MB

package org.primefaces.showcase.view.message;
 
import javax.faces.application.FacesMessage;
import javax.faces.bean.ManagedBean;
import javax.faces.context.FacesContext;
 
@ManagedBean
public class GrowlView {
     
    private String message;
 
    public String getMessage() {
        return message;
    }
 
    public void setMessage(String message) {
        this.message = message;
    }
     
    public void saveMessage() {
        FacesContext context = FacesContext.getCurrentInstance();
         
        context.addMessage(null, new FacesMessage("Successful",  "Your message: " + message) );
        context.addMessage(null, new FacesMessage("Second Message", "Additional Message Detail"));
    }
}

Message

<p:tooltip />
         
<h:form>
    <p:messages id="messages" showDetail="true" autoUpdate="true" closable="true" />
 
    <p:commandButton value="Info" actionListener="#{messagesView.info}" />
    <p:commandButton value="Warn" actionListener="#{messagesView.warn}" />
    <p:commandButton value="Error" actionListener="#{messagesView.error}" />
    <p:commandButton value="Fatal" actionListener="#{messagesView.fatal}" />
</h:form>
 
<p:separator />
 
<h:form>
    <h:panelGrid id="grid" columns="3" cellpadding="5">
        <p:outputLabel for="default" value="Default:" />
        <p:inputText id="default" required="true" />
        <p:message for="default" />
 
        <p:outputLabel for="txt" value="Text:" />
        <p:inputText id="txt" required="true" />
        <p:message for="txt" display="text" />
 
        <p:outputLabel for="icon" value="Icon:" />
        <p:inputText id="icon" required="true" />
        <p:message for="icon" display="icon" />
 
        <p:outputLabel for="tt" value="Tooltip:" />
        <p:inputText id="tt" required="true" />
        <p:message for="tt" display="tooltip" />
    </h:panelGrid>
 
    <p:commandButton id="submitButton" value="Submit" update="grid" />
</h:form>

Message MB

package org.primefaces.showcase.view.message;
 
import javax.faces.application.FacesMessage;
import javax.faces.bean.ManagedBean;
import javax.faces.context.FacesContext;
 
@ManagedBean
public class MessagesView {
     
    public void info() {
        FacesContext.getCurrentInstance().addMessage(null, new FacesMessage(FacesMessage.SEVERITY_INFO, "Info", "PrimeFaces Rocks."));
    }
     
    public void warn() {
        FacesContext.getCurrentInstance().addMessage(null, new FacesMessage(FacesMessage.SEVERITY_WARN, "Warning!", "Watch out for PrimeFaces."));
    }
     
    public void error() {
        FacesContext.getCurrentInstance().addMessage(null, new FacesMessage(FacesMessage.SEVERITY_ERROR, "Error!", "Contact admin."));
    }
     
    public void fatal() {
        FacesContext.getCurrentInstance().addMessage(null, new FacesMessage(FacesMessage.SEVERITY_FATAL, "Fatal!", "System Error"));
    }
}

Saludos.