Prayer to ask or to thank
If not a regular, household ritual (ie, it is not in honour of household divinities) prayers and offerings are generally best performed outdoors under an open sky, preferably in a place which seems to be associated with the Deity. Creating a shrine, of either a temporary or permanent nature is a possibility when a sacred location cannot be identified.
It is important to prepare for rituals. Some of the things you may want to consider are as follows:
Determining what it is that you want, and thus who are the appropriate Deities to supplicate. To identify the Deity the following posts may be helpful: Contemporary Visions of the Divine and A Long List of Deities.
Determining whether the Deity to supplicate is primarily celestial (of the sky), aquatic (of water) or chthonic (of the earth). If celestial, normally a ritual fire should be lit and offerings burnt in this fire. The ritual should normally be performed in the day, but not if it is windy. Safety dictates that you bring a fire blanket or jug of water in case the fire becomes unsafe. If aquatic, normally offerings will be poured or thrown into the body of water most close to the Deity (eg, if Neptune, the ocean; if a river spirit, in the river). If chthonic, normally offerings will be poured into the earth or a pit is dug into which offerings are placed, such offerings may be burnt whole in that place or merely buried. Alternately (a) food, liquid or plant offerings can be symbolically placed on a plate before an image or object associated with the Deity; (b) incense may be burnt at the Deity’s shrine; (c) ornaments, garlands or other objects may be placed around the statue of the Deity; (d) offerings specific to the Deity may be made – embroidery honours Minerva; smithing honours Vulcan; music honours Apollo; eloquent prose honours Mercury; the very act of drinking wine may honour Bacchus; sexual acts may honour fertility Deities, and so on. See Pagan Offerings to the Gods for more on suitable offerings.
Note that in the Roman tradition offerings are normally made to Janus before other Gods, because he is the gateway to the divine, while Vesta, Goddess of altar and hearth fire, receives the last offering (Cicero, On the Nature of the Gods), though Vesta’s name may be invoked first at the start of the ritual (Ovid, Fasti). Arguably, Vesta need not be invoked if the ritual involves no fire.
It is advisable to prepare what you will do and say so that the ritual does not become fumbling or ineffective. Note that you should speak in a clear voice; stumbling over words in the midst of a ritual is not desirable and may even be regarded as inauspicious. It is perfectly fine to read from a prepared script during the ritual – in fact this may be preferable.
Hands and clothes should be clean (the cleaner you are the better), normally white clothes will preferable, and the head is usually covered when praying to Roman Gods (notable exceptions to this general rule include Saturn and Hercules, to whom the ritus Graecus applies – note that despite the name the ritus Graecus in fact refers to a style of Roman ritual, which is inspired by, but not identical to, Hellenic rites; it may involve wearing a laurel wreath). You do not need to wear a toga (traditionally a fold of the toga would be placed over the head) – a hoodie with the hood up is sufficient. Otherwise a scarf or shawl. Only the back of the head needs covering; the greater part of the arms and neck can be left exposed.
Prayers should be made with open palms (both hands or the right hand only), fingers together and stretched slightly backwards. The palm of the right hand (or both hands) should be facing the presumed abode of the God/s being honoured (eg, the sky for celestial Gods and the ground for chthonic Gods) or at an image of the God or shrine to the God.
Some tips for a small, outdoor fire ceremony (feel free to disregard – this is tailored for a city dweller to perform on an apartment balcony): before starting the fire line the bowl/container in which the flame will burn with aluminium foil and place a small tea light in the middle. Light the candle then place very small broken up twigs (up to 2 inches long) and dried leaves over the flame. Do not place too much fuel in the bowl as the fire will grow too large. Keep a large jug of water handy. Do not perform this ceremony on a windy day.
The following words are the kind of things you might say during Roman rites, but of course your own prayers might be worded completely differently. The key words may include (1) correct identification of the God you wish to honour (hence the name of the Deity and a description of their domain), (2) a clear statement of what you are praying for, and (3) a clear description of what offerings you are making or will make should your prayer be answered.
Offer a gesture of respect (eg, kissing the right hand, or the fingers of the right hand, or blowing a kiss towards the presumed abode of the God/s) and ignite the flame as you say something like:
Be well, revered Vesta, Goddess of the flame, may you look favourably upon this rite.
Make the first offering to Janus (eg, incense) and say (something like):
Janus, or whatever name it is that you prefer, gate keeper and opener of the way, may this incense find favour with you.
Divine Janus, may you be well, may you look favourably upon me, may this incense find favour with you.
Prayer – pray with open palm/s (both hands or the right hand only), fingers together, and stretched slightly backward (the following prayers are merely suggestive of the kinds of things you might like to say):
Noble [name Deity], or whatever name it is that you prefer, God or Goddess of [name Deity attributes], I pray to you, I do you reverence. I ask your grace and favour that you might [state your request]. May you know the sincerity of my request by this [offering, eg, honey] that I offer; may it find favour with you.
Divine [name Deity], may you be well, may you look kindly on me. I ask that you might [state your request]. May you know the sincerity of my request by this [offering, eg, honey] that I offer; may it find favour with you.
Make a final offering to Vesta (eg, incense), and pray (something like):
Revered Vesta, may you look favourably upon me, if I have done anything to violate this rite may you receive this incense in expiation of my error.
Offer a gesture of respect (eg, blow a kiss) and announce:
It is done.
Vows and oaths
Before making a vow or oath you may first perform steps 1-2 of the prayer above, or you may simply state the words below (adapted to your own circumstances) – whatever feels right.
Vow to offer – if making a vow to make an offering to a Deity in the future touch your chest while saying (the following are merely suggestive of the kinds of things you might like to say):
Noble [name Deity being addressed], or whatever name it is that you prefer, God or Goddess of [name Deity attributes], may you allow [state desired outcome]. If you let me know, feel and understand that you have brought this about let it be understood that I will [state offering that will be forthcoming]. I call on you to witness [name Deity/ies, eg, Mother Earth].
Divine [name Deity being addressed], may you be well, may you look favourably upon me; may you allow [state desired outcome]. If you let me know, feel and understand that you have brought this about let it be understood that I will [state offering that will be forthcoming].
Sacred oath – if making a sacred oath touch your chest while saying (again the wording is merely suggestive of how you might choose to formulate an oath):
Noble [name Deity being addressed], or whatever name it is that you prefer, God or Goddess of [name Deity attributes], I swear that I will [state nature of pledge]. If I do not do not this thing may [state punishment you seek to be delivered unto yourself if the oath is broken]. I call on you to witness [name Deity/ies, eg, Mother Earth].
Divine [name Deity being addressed], may you be well, may you look favourably upon me. To you I swear that I will [state nature of pledge]. If I do not do not this thing may [state punishment you seek to be delivered unto yourself if the oath is broken].
You may now perform the last two steps of the prayer of request/gratitude, as above, if you want to.
As for ideas for how to word daily prayers see Household Shrine and Ritual.