Sorry I am not a pandit :-) but just thought to share some of the Popular Shlokas and their Meanings

These are some of the Sholakas that we would have come across. 
We wouldnt have known as to what they mean actually.
I have mentioned only some of the popular ones with their meanings.
Please find some time to go thorough them and also follow it.

1. In Sanskrit : 
शुक्लाम्बरधरं देवं शशिवर्णं चतुर्भुजम् |
प्रसन्नवदनं ध्यायेत् सर्वविघ्नोपशान्तये || ||

In English :
Shuklambara Dharam Vishnum
Shashivarnam Chatur Bhujam
Prasanna Vadannam Dhyayet
Sarva Vignopa Santaye

Translation :
In order to remove all obstacles, one should meditate on
(the God Ganesha) as wearing a white garment, as having the
complexion like the moon,and having four arms and a pleasant
countenance.


2. In Sanskrit :
ॐ भूर्भुवः स्वः तत्सवितुर्वरेण्यम्
भर्गो देवस्य धीमहि धियो यो नः प्रचोदयात् || ||

In English :
Om Burbuvah swaha Tatsavithurvarenyum
Bargo Devasya dhimahi dhiyo yo naha prachodayath

Translation :
OM. I adore the Divine Self who illuminates the three worlds --
physical, astral and causal;I offer my prayers to that
God who shines like the Sun. May He enlighten our intellect.
This mantra is considered to be the greatest of all Mantras.
Those who repeat this mantra with devotion develop
 a brilliant intellect. This Mantra grants health of body and
mind, and also success, peace, prosperity and spiritual
enlightment.


3. In Sanskrit :
वक्रतुंड महाकाय कोटिसूर्यसमप्रभ |
निर्विघ्नं कुरु मे देव सर्वकार्येषु सर्वदा || ||

In English :
Sri Vakratunda Mahakaaya Koti-soorya samaprabha
Nirvighnam kuru me Deva Sarva-karyeshu Sarvadaa


Translation :
O Lord Ganesha, of huge body with elephant head,
shining like billions of suns, O God,remove all
obstacles from my endeavors, forever.(Alternate)
Oh! Lord (Ganesha), of huge body and curved
elephant trunk,whose brilliance is equal to billions
of suns, always remove all obstacles from my
endeavors.


4. In Sanskrit :
मूषिकवाहन् मोदकहस्त चामरकर्ण विलम्बित सूत्र |
वामनरूप महेश्वरपुत्र विघ्नविनायक पाद नमस्ते || ||

In English :
Mooshika vahana modaka hasta
Chamara karna vilambita sootra
Vamana roopa Maheswara putra 
Vigna-vinayaka paada namaste

Translation :
Oh God  who has the mouse as his vehicle,
and the sweet modhaka (rice ball) in your hand,
whose ears are wide like fans, wearing the
sacred thread. Oh son of Lord Shiva who is of
short stature and who removes all obstacles,
Lord Vinayaka,I  bow at your feet.

5.In Sanskrit :
एकदंताय विद्महे | वक्रतुंडाय धीमहि |
तन्नो दंती प्रचोदयात् || ||

In English :
Ekadantaya vidmahe  vakra thundaya dhimahi
Thanno dhanthi prachodhayat

Translation :
(This is a typical Vedic dialog where puzzles
are posed and solved. they are always recited
by alternate groups as below.)
Poser:  We know of one with just one tooth! 
Responder: Yes,we think of the one with a bent mouth.
Together: May he, the one known as dantii
(One with the tooth) awaken us (to the ultimate truth).

6. In Sanskrit :
गुरुर्ब्रह्मा गुरुर्विष्णूः गुरुर्देवो महेश्वरः |
गुरुः साक्षात् परब्रह्म तस्मै श्रीगुरवे नमः || ||

In English :
Gurur Brahma Gurur Vishnu
Gurur Devo Maheshvarah
Guru Shakshat Param Brahma 
Tasmai Sri Gurave Namah

Translation :
Guru is indeed the Creator in the form
Lord Brahma,he is indeed the Sustainer as
Lord Vishnu,and Destroyer as Lord Shiva,
in fact he is the limitless Brahman,
I salute to such a Guru!(Alternate)
Salutations to the Guru who is himself Brahma,
 the creator,VishNu, the protector and Shiva,
the destroyer.Who is none other than the
limitless great Brahman.To Him are all
my salutations.


7. In Sanskrit :
श्रियः कान्ताय कल्याण निधये निधयेर्थिनाम् |
श्री वेङ्कट निवासाय श्रीनिवासाय मङ्गळम् || ||

In English :
Shreeyah Kanthaya Kalyana
nidhaye nidhayerthinaam
Shree Venkata Nivasaya Shrinavasaya Mangalam

Translation :
Glory to the Lord vishhNu, who is the consort of
mahaalakshmii, and the treasure  trove of
auspiciousness, who grants wealth to all
seekers of material wealth, who resides in the
venkata mountains and in whose heart,
mahalakshmi who symbolises wealth resides.


8. In Sanskrit :
नारायणाय विद्महे | वासुदेवाय धीमहि |
तन्नो विष्णुः प्रचोदयात् || ||

In English :
Narayanaya Vidhmahe Vasudevaya Dhimahi 
Thanno Vishnuh Prachodhayath

Translation :
This is my offering to the Lord naaraayaNaa
who is present in all his creations.
I meditate to the son of vasudevaa,
who is all pervasive. Let that omnipresent
Lord inspire me.

9. In Sanskrit :
ॐ त्रयम्बकं यजामहे
सुगन्धिं पुष्टिवर्धनम् |
उर्वारुकमिव बन्धनान्
मृत्योर्मुक्षीय मामृतात् || ||

In English :
Om Trayambakam Yajamahe 
Sugandhim Pushtivardhanam 
Urva-rukamiva Bhandhanaat 
Mrityor-mukshiya ma amritat

Translation :
This is the Maha Mrityunjaya Mantra.
We worship the three-eyed One (Lord Siva)
Who is fragrant and who nourishes well all beings;
may He liberate us from death for the sake 
of Immortality even as the cucumber
is severed from its bondage (to the creeper).


10. In Sanskrit :
सर्वे भवंतु सुखिनः सर्वे संतु निरामयाः |
सर्वे भद्राणि पश्यंतु मा कश्चिद् दुःखभाग्भवेत् || ||

In English :
Sarve Bhavantu Sukhinaha Sarve Santu Niramayah
Sarve Bhadrani Pashyantu Mas Kaschid Dhuka Bhag Bhavet

Translation :
May everybody be happy, may everybody
be free from disease, may everybody see goodness,
may none fall on evil days.


11. In Sanskrit :
ॐ असतो मा सद्गमय | तमसो मा ज्योतिर्गमय |
मृत्योर्मा अमृतं गमय |
ओम शांतिः शांतिः शांतिः || ||
In English :
Om Asatho ma sadhgamaya
Thamaso ma jyothirgamaya 
mruthyorma amrutham gamaya 
om shanthi shanthi shanthihi

Translation :
Om Lead us from untruth to truth, from
darkness to light,from death to immortality.
Om Peace Peace Peace.


12. In Sanskrit :
कर्मण्येवाधिकारस्ते मा फलेषु कदाचन |
मा कर्मफलहेतुर्भिः मा ते सङ्गोस्त्व कर्मणि || ||

In English :
Karmanye vadhikarasthe ma phaleshu kadhachan
Ma karmaphalahethurbi ma the sangosthava karmani

Translation :
You have right over your respective duty only,
but no control or claim over the results.
The fruits of work should not be your motive.
You should never be inactive.


13. In Sanskrit :
योगेन चित्तस्य पदेन वाचः मलं शरीरस्य च वैद्यकेन |
योपाकरोत्तं प्रवरं मुनीनां पतंजलिं
प्रांजलिरानतोऽस्मि || ||

In English :
Yogena chitasya padena vaachah Malam
sharirasya cha vaidyakena
yopathkarotham pravaram muninaha
Pathanjalim pranjaliranathosmi

Translation :
With joined hands, I stay bowed to Patanjali-
the pereminent among the sages,
who removed the impurities of the mind by
(explaining) yoga, of the speech by
(commenting on) grammar and of the body by
(expounding) medicine.


14. In Sanskrit :
   ॐ सहना ववातु; सहनू भुनक्तु
  सहवीर्यम करवावहै ;
     तेजस विनावती तमास्तुमा विध्विशावाहाई || ||

In English :
Om Sahana Vavatu Sahanau Bhunaktu
Sahaveeryam Karavavahai Tejas Vinavati
Tamastuma vidhwishavahai
Om Shanti Shanti Shantihi

Translation :
May He protect both of us.
May He nourish both of us.
May we both acquire the capacity
 (to study and understand the scriptures).
May our study be brilliant.
May we not argue with each other.
Om peace, peace, peace.


15. In Sanskrit :
  ग्न्यानान्धामायाम धेवं
  निर्मला स्पदिकक्रिथिम
   आधाराम सर्वविध्यनाम
    हयग्रीव मुबास्माहे || ||

In English :
Hyagreevar Shlokam
(This sloka is to be recited before children
 start their daily school work/studies)  
Gyaananandamayam Devam
 Nirmala Spadikakruthim
Aadaram Sarva Vidyanaam
Hyagreevam Upasmahe

Translation :
Vidyaarambam begins with a prayer to
Sri Hyagreeva (Lord with the Horse’s face)
Haya-horse; greeva-neck.
You are the presiding deity for all knowledge.
We pray to you to bless us with all the knowledge.

Happy Praying with faith and belief.